Open in CoCalc
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@Article{ agashe,
3
author = {Agashe, A.},
4
title = {On invisible elements of the {T}ate-{S}hafarevich group},
5
journal = {C. R. Acad. Sci. Paris S\'er. I Math.},
6
fjournal = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
7
Math\'ematique},
8
volume = {328},
9
year = {1999},
10
number = {5},
11
pages = {369--374},
12
issn = {0764-4442},
13
coden = {CASMEI},
14
mrclass = {11Gxx},
15
mrnumber = {1 678 131}
16
}
17
18
@Article{ agashe-stein:bsd,
19
author = "Agashe, A. and Stein, W.\thinspace{}A.",
20
title = "Visible {E}vidence for the {B}irch and {S}winnerton-{D}yer
21
{C}onjecture for {M}odular {A}belian {V}arieties of
22
{A}nalytic {R}ank~$0$",
23
date = 2003,
24
journal = {To appear in Math. of Computation}
25
}
26
27
@Article{ agashe-stein:manin,
28
author = "Agashe, A. and Stein, W.\thinspace{}A.",
29
title = "The Manin Constant, Congruence Primes, and the Modular
30
Degree",
31
year = {2004},
32
journal = {Preprint,\hfill\\ {\tt
33
http://modular.fas.harvard.edu/papers/manin-agashe/}}
34
}
35
36
@Article{ agashe-stein:schoof-appendix,
37
author = {Lario, J.-C. and Schoof, R.}},
38
title = {Some computations with {H}ecke rings and deformation
39
rings},
40
note = {With an appendix by Amod Agashe and William Stein},
41
journal = {Experiment. Math.},
42
fjournal = {Experimental Mathematics},
43
volume = {11},
44
year = {2002},
45
number = {2},
46
pages = {303--311},
47
issn = {1058-6458},
48
mrclass = {11F80 (11F11 11F25)},
49
mrnumber = {2004b:11072},
50
mrreviewer = {Lea Terracini}
51
}
52
53
@Article{ agashe-stein:visibility,
54
author = {Agashe, A. and Stein, W.\thinspace{}A.},
55
title = {Visibility of {S}hafarevich-{T}ate groups of abelian
56
varieties},
57
journal = {J. Number Theory},
58
fjournal = {Journal of Number Theory},
59
volume = {97},
60
year = {2002},
61
number = {1},
62
pages = {171--185},
63
issn = {0022-314X},
64
coden = {JNUTA9},
65
mrclass = {11G40 (11G10 14K15)},
66
mrnumber = {2003h:11070},
67
mrreviewer = {Chandan Singh Dalawat}
68
}
69
70
@Article{ agashe:invisible,
71
author = {Agash{\'e}, Amod},
72
title = {On invisible elements of the {T}ate-{S}hafarevich group},
73
journal = {C. R. Acad. Sci. Paris S\'er. I Math.},
74
fjournal = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
75
Math\'ematique},
76
volume = {328},
77
year = {1999},
78
number = {5},
79
pages = {369--374},
80
issn = {0764-4442},
81
coden = {CASMEI},
82
mrclass = {11G40 (11G10 11G18)},
83
mrnumber = {2000e:11083},
84
mrreviewer = {Kenneth Kramer}
85
}
86
87
@Article{ agashe:phd,
88
author = "Agashe, A.",
89
title = {The {B}irch and {S}winnerton-{D}yer formula for modular
90
abelian varieties of analytic rank~$0$},
91
journal = {Ph.D. thesis, University of California, Berkeley},
92
year = {2000}
93
}
94
95
@Book{ antwerpiv,
96
title = {Modular functions of one variable. {I}{V}},
97
booktitle = {Proceedings of the International Summer School on Modular
98
Functions of One Variable and Arithmetical Applications,
99
RUCA, University of Antwerp, Antwerp, July 17--August 3,
100
1972},
101
editor = {Birch, B.\thinspace{}J. and Kuyk, W.},
102
note = {Lecture Notes in Mathematics, Vol. 476},
103
publisher = {Springer-Verlag},
104
address = {Berlin},
105
year = {1975},
106
pages = {iv+151}
107
}
108
109
@Article{ artin:conjecture,
110
author = {Artin, E.},
111
title = {{\"U}ber eine neue {A}rt von {L}-Reihen},
112
journal = {Abh. Math. Sem. Univ. Hamburg},
113
volume = {3},
114
year = {1923 or 1924??? CHECK!},
115
pages = {89--108}
116
}
117
118
@Article{ artin:conjecture2,
119
author = {Artin, E},
120
title = {Zur {T}heorie der {L}-{R}eihen mit allgemeinen
121
{G}ruppencharakteren},
122
journal = {Abh. math. Semin. Univ. Hamburg},
123
volume = {8},
124
year = {1930},
125
pages = {292--306}
126
}
127
128
@Article{ ash-stevens,
129
author = {Ash, A. and Stevens, G.},
130
title = {Cohomology of arithmetic groups and congruences between
131
systems of {H}ecke eigenvalues},
132
journal = {J. Reine Angew. Math.},
133
fjournal = {Journal f\"ur die Reine und Angewandte Mathematik},
134
volume = {365},
135
year = {1986},
136
pages = {192--220},
137
issn = {0075-4102},
138
coden = {JRMAA8}
139
}
140
141
@Article{ atkin-lehner,
142
author = {Atkin, A.\thinspace{}O.\thinspace{}L. and Lehner, J.},
143
title = {Hecke operators on \protect{$\Gamma \sb{0}(m)$}},
144
journal = {Math. Ann.},
145
volume = {185},
146
year = {1970},
147
pages = {134--160}
148
}
149
150
@Article{ bdsbt,
151
author = {Buzzard, K. and Dickinson, M. and Shepherd-Barron, N. and
152
Taylor, R.},
153
title = {On icosahedral {A}rtin representations},
154
journal = { \protect{\tt
155
http://www.math.harvard.edu/HTML/Individuals/Richard\_Taylor.html}}
156
,
157
date = {2000}
158
}
159
160
@Book{ bgr,
161
author = {Bosch, S. and G{\"u}ntzer, U. and Remmert, R.},
162
title = {Non-{A}rchimedean analysis: A systematic approach to rigid
163
analytic geometry},
164
publisher = {Springer-Verlag},
165
address = {Berlin},
166
year = {1984},
167
pages = {xii+436},
168
isbn = {3-540-12546-9},
169
mrclass = {32K10 (30G05 46P05)},
170
mrnumber = {86b:32031},
171
mrrevr = {W. Bartenwerfer}
172
}
173
174
@InCollection{ birch:atkin,
175
author = {Birch, B.},
176
title = {Atkin and the {A}tlas {L}ab},
177
booktitle = {Proceedings of the conference in honor of
178
A.\thinspace{}O.\thinspace{}L. Atkin held at the University
179
of Illinois, Chicago, IL, September 1995},
180
pages = {13--20},
181
publisher = {Amer. Math. Soc.},
182
address = {Providence, RI},
183
year = {1998},
184
mrclass = {11-03 (01A60 11F30 11F33)},
185
mrnumber = {99c:11002},
186
mrrevr = {V. Kumar Murty}
187
}
188
189
@InCollection{ birch:bsd,
190
author = {Birch, B.\thinspace{}J.},
191
title = {Elliptic curves over \protect{${\mathbf{Q}}$: {A}}
192
progress report},
193
booktitle = {1969 Number Theory Institute (Proc. Sympos. Pure Math.,
194
Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969)},
195
pages = {396--400},
196
publisher = {Amer. Math. Soc.},
197
address = {Providence, R.I.},
198
year = {1971}
199
}
200
201
@InCollection{ birch:cyclo,
202
author = {Birch, B.\thinspace{}J.},
203
title = {Cyclotomic fields and {K}ummer extensions},
204
booktitle = {Algebraic Number Theory (Proc. Instructional Conf.,
205
Brighton, 1965)},
206
pages = {85--93},
207
publisher = {Thompson, Washington, D.C.},
208
year = {1967}
209
}
210
211
@InCollection{ birch:edsac,
212
author = {Birch, B. J.},
213
title = {Conjectures concerning elliptic curves},
214
booktitle = {Proceedings of Symposia in Pure Mathematics, VIII},
215
pages = {106--112},
216
publisher = {Amer. Math. Soc.},
217
address = {Providence, R.I.},
218
year = {1965},
219
mrclass = {14.49 (14.40)},
220
mrnumber = {30 \#4759},
221
mrreviewer = {J. W. S. Cassels}
222
}
223
224
@InCollection{ birch:hecke_actions,
225
author = {Birch, B. J.},
226
title = {Hecke actions on classes of ternary quadratic forms},
227
booktitle = {Computational number theory (Debrecen, 1989)},
228
pages = {191--212},
229
publisher = {de Gruyter},
230
address = {Berlin},
231
year = {1991},
232
mrclass = {11E45 (11E20 11F11 11G05 11Y35)},
233
mrnumber = {93i:11047},
234
mrrevr = {Rainer Schulze-Pillot}
235
}
236
237
@InCollection{ bloch-kato,
238
author = {Bloch, S. and Kato, K.},
239
title = {\protect{${L}$}-functions and \protect{T}amagawa numbers
240
of motives},
241
booktitle = {The Grothendieck Festschrift, Vol. \protect{I}},
242
pages = {333--400},
243
publisher = {Birkh\"auser Boston},
244
address = {Boston, MA},
245
year = {1990}
246
}
247
248
@Article{ bockle:density,
249
author = {B{\"o}ckle, Gebhard},
250
title = {On the density of modular points in universal deformation
251
spaces},
252
journal = {Amer. J. Math.},
253
fjournal = {American Journal of Mathematics},
254
volume = {123},
255
year = {2001},
256
number = {5},
257
pages = {985--1007},
258
issn = {0002-9327},
259
coden = {AJMAAN},
260
mrclass = {11F80},
261
mrnumber = {1 854 117}
262
}
263
264
@Article{ bolling:sha,
265
author = {B{\"o}lling, Reinhard},
266
title = {Die {O}rdnung der {S}chafarewitsch-{T}ate-{G}ruppe kann
267
beliebig gro\ss \ werden},
268
journal = {Math. Nachr.},
269
volume = {67},
270
year = {1975},
271
pages = {157--179},
272
mrclass = {14K15},
273
mrnumber = {52 \#5684},
274
mrreviewer = {J. W. S. Cassels}
275
}
276
277
@Proceedings{ boston,
278
title = {Modular forms and \protect{F}ermat's last theorem
279
(Boston,MA, 1995)},
280
editor = {Cornell, G. and Silverman, J.\thinspace{}H. and Stevens,
281
G.},
282
note = {Papers from the Instructional Conference on Number Theory
283
and Arithmetic Geometry held at Boston University, Boston,
284
MA, August 9--18, 1995},
285
publisher = {Springer-Verlag},
286
address = {New York},
287
year = {1997},
288
pages = {xx+582},
289
isbn = {0-387-94609-8}
290
}
291
292
@Article{ boston-lenstra-ribet,
293
author = {N. Boston and \protect{H.\thinspace{}W. Lenstra, Jr.} and
294
K.\thinspace{}A. Ribet},
295
title = {Quotients of group rings arising from two-dimensional
296
representations},
297
journal = {C. R. Acad. Sci. Paris S\'er. I Math.},
298
fjournal = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
299
Math\'ematique},
300
volume = {312},
301
year = {1991},
302
number = {4},
303
pages = {323--328},
304
issn = {0764-4442},
305
coden = {CASMEI}
306
}
307
308
@Article{ breuil-conrad-diamond-taylor,
309
author = {Breuil, C. and Conrad, B. and Diamond, F. and Taylor, R.},
310
title = {On the modularity of elliptic curves over {$\bold Q$}:
311
wild 3-adic exercises},
312
journal = {J. Amer. Math. Soc.},
313
fjournal = {Journal of the American Mathematical Society},
314
volume = {14},
315
year = {2001},
316
number = {4},
317
pages = {843--939 (electronic)},
318
issn = {0894-0347},
319
mrclass = {11G05 (11F80 11G07 14G35)},
320
mrnumber = {2002d:11058},
321
mrreviewer = {Karl Rubin}
322
}
323
324
@Article{ brue,
325
author = {Brueggeman, S.},
326
title = {The non-existence of certain \protect{Galois} extensions
327
unramified outside 5},
328
journal = {Journal of Number Theory},
329
volume = {75},
330
year = {1999},
331
pages = {47--52}
332
}
333
334
@Article{ brumer-mcguinness,
335
author = {Brumer, A. and McGuinness, O.},
336
title = {The behavior of the {M}ordell-{W}eil group of elliptic
337
curves},
338
journal = {Bull. Amer. Math. Soc. (N.S.)},
339
fjournal = {American Mathematical Society. Bulletin. New Series},
340
volume = {23},
341
year = {1990},
342
number = {2},
343
pages = {375--382},
344
issn = {0273-0979},
345
coden = {BAMOAD},
346
mrclass = {11G40 (11-04 11G05)},
347
mrnumber = {91b:11076},
348
mrreviewer = {Kenneth Kramer},
349
note = {\protect{\tt http://shimura.math.berkeley.edu/\~{ }oisin/}}
350
}
351
352
@Article{ brumer:rank,
353
author = {Brumer, A.},
354
title = {The rank of \protect{${J}\sb 0({N})$}},
355
note = {Columbia University Number Theory Seminar (New York,
356
1992)},
357
journal = {Ast\'erisque},
358
fjournal = {Ast\'erisque},
359
number = {228},
360
year = {1995},
361
pages = {3, 41--68},
362
issn = {0303-1179}
363
}
364
365
@Article{ buhler-gross,
366
author = {Buhler, J.\thinspace{}P. and Gross, B.\thinspace{}H.},
367
title = {Arithmetic on elliptic curves with complex multiplication.
368
{I}{I}},
369
journal = {Invent. Math.},
370
fjournal = {Inventiones Mathematicae},
371
volume = {79},
372
year = {1985},
373
number = {1},
374
pages = {11--29},
375
issn = {0020-9910},
376
coden = {INVMBH},
377
mrclass = {11G40 (11G05 14K22)},
378
mrnumber = {86j:11066},
379
mrreviewer = {Kenneth Kramer}
380
}
381
382
@Book{ buhler:thesis,
383
author = {Buhler, J.\thinspace{}P.},
384
title = {Icosahedral \protect{G}alois representations},
385
note = {Lecture Notes in Mathematics, Vol. 654},
386
publisher = {Springer-Verlag},
387
address = {Berlin},
388
year = {1978},
389
pages = {ii+143},
390
isbn = {3-540-08844-X}
391
}
392
393
@Article{ bump-friedberg-hoffstein,
394
author = {Bump, D. and Friedberg, S. and Hoffstein, J.},
395
title = {Eisenstein series on the metaplectic group and
396
nonvanishing theorems for automorphic
397
\protect{${L}$}-functions and their derivatives},
398
journal = {Ann. of Math. (2)},
399
fjournal = {Annals of Mathematics. Second Series},
400
volume = {131},
401
year = {1990},
402
number = {1},
403
pages = {53--127},
404
issn = {0003-486X},
405
coden = {ANMAAH}
406
}
407
408
@Article{ buzzard-stein:artin,
409
author = {Buzzard, K. and Stein, W.\thinspace{}A.},
410
title = {A mod five approach to modularity of icosahedral {G}alois
411
representations},
412
journal = {Pacific J. Math.},
413
fjournal = {Pacific Journal of Mathematics},
414
volume = {203},
415
year = {2002},
416
number = {2},
417
pages = {265--282},
418
issn = {0030-8730},
419
coden = {PJMAAI},
420
mrclass = {11F80},
421
mrnumber = {2003c:11052},
422
mrreviewer = {Mark Edward Tristan Dickinson}
423
}
424
425
@Article{ buzzard-taylor,
426
author = {Buzzard, K. and Taylor, R.},
427
title = {Companion forms and weight one forms},
428
journal = {Ann. of Math. (2)},
429
fjournal = {Annals of Mathematics. Second Series},
430
volume = {149},
431
year = {1999},
432
number = {3},
433
pages = {905--919},
434
issn = {0003-486X},
435
coden = {ANMAAH},
436
mrclass = {11Fxx},
437
mrnumber = {1 709 306}
438
}
439
440
@Article{ buzzard:level,
441
author = {Buzzard, K.},
442
title = {On level-lowering for mod 2 representations},
443
journal = {preprint}
444
}
445
446
@Article{ buzzard:t2,
447
author = {Buzzard, Kevin},
448
title = {On the eigenvalues of the {H}ecke operator {$T\sb 2$}},
449
journal = {J. Number Theory},
450
fjournal = {Journal of Number Theory},
451
volume = {57},
452
year = {1996},
453
number = {1},
454
pages = {130--132},
455
issn = {0022-314X},
456
coden = {JNUTA9},
457
mrclass = {11F25},
458
mrnumber = {96m:11033},
459
mrreviewer = {Thomas R. Shemanske}
460
}
461
462
@Article{ carayol:modell,
463
author = {Carayol, H.},
464
title = {Sur les \protect{repr\'esentations} galoisiennes modulo
465
\protect{$\ell$ attach\'ees} aux formes modulaires},
466
journal = {Duke Math. J.},
467
volume = {59},
468
year = {1989},
469
pages = {785--801}
470
}
471
472
@Article{ carearly,
473
author = "Carayol, H.",
474
title = {Sur les \protect{repr\'esentations}
475
\protect{$\ell$-adiques} \protect{associ\'ees} aux formes
476
modulaires de \protect{Hilbert}},
477
journal = {Ann. scient. \protect{\'Ec.} Norm. Sup., \protect{$4^{\rm
478
eb}$ s\'erie}},
479
volume = {19},
480
year = {1986},
481
pages = {409--468}
482
}
483
484
@InProceedings{ casselman,
485
author = {Casselman, W.},
486
title = {On representations of \protect{${\rm {G}{L}}\sb{2}$} and
487
the arithmetic of modular curves},
488
booktitle = {Modular functions of one variable, II (Proc. Internat.
489
Summer School, Univ. Antwerp, Antwerp, 1972)},
490
pages = {107--141. Lecture Notes in Math., Vol. 349},
491
publisher = {Springer},
492
address = {Berlin},
493
year = {1973}
494
}
495
496
@Book{ cassels-flynn,
497
author = {Cassels, J.\thinspace{}W.\thinspace{}S. and Flynn,
498
E.\thinspace{}V.},
499
title = {Prolegomena to a middlebrow arithmetic of curves of genus
500
\protect{$2$}},
501
publisher = {Cambridge University Press},
502
address = {Cambridge},
503
year = {1996},
504
pages = {xiv+219},
505
isbn = {0-521-48370-0},
506
mrclass = {11G30 (11Y50 14G25)},
507
mrnumber = {97i:11071},
508
mrrevr = {Joseph H. Silverman}
509
}
510
511
@Proceedings{ cassels-frohlich,
512
title = {Algebraic number theory},
513
booktitle = {Proceedings of the instructional conference held at the
514
University of Sussex, Brighton, September 1--17, 1965},
515
editor = {Cassels, J.\thinspace{}W.\thinspace{}S. and
516
\protect{Fr{\"o}hlich}, A.},
517
note = {Reprint of the 1967 original},
518
publisher = {Academic Press Inc. [Harcourt Brace Jovanovich
519
Publishers]},
520
address = {London},
521
year = {1986},
522
pages = {xviii+366},
523
isbn = {0-12-163251-2}
524
}
525
526
@Article{ cassels:arithmeticiii,
527
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
528
title = {{A}rithmetic on curves of genus $1$. {I}{I}{I}. {T}he
529
{T}ate-\v {S}afarevi\v c and {S}elmer groups},
530
journal = {Proc. London Math. Soc. (3)},
531
volume = {12},
532
year = {1962},
533
pages = {259--296},
534
mrclass = {14.49},
535
mrnumber = {29 \#1212}
536
}
537
538
@Article{ cassels:arithmeticiv,
539
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
540
title = {Arithmetic on curves of genus \protect{$1$}. {I}{V}.
541
{P}roof of the {H}auptvermutung},
542
journal = {J. Reine Angew. Math.},
543
volume = {211},
544
year = {1962},
545
pages = {95--112}
546
}
547
548
@Article{ cassels:arithmeticv,
549
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
550
title = {Arithmetic on curves of genus 1. {V}. {T}wo
551
counterexamples},
552
journal = {J. London Math. Soc.},
553
volume = {38},
554
year = {1963},
555
pages = {244--248}
556
}
557
558
@Article{ cassels:bigsha,
559
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
560
title = {Arithmetic on curves of genus $1$. {V}{I}. {T}he {T}ate-\v
561
{S}afarevi\v c group can be arbitrarily large},
562
journal = {J. Reine Angew. Math.},
563
volume = {214/215},
564
year = {1964},
565
pages = {65--70},
566
mrclass = {14.49 (10.12)},
567
mrnumber = {29 \#104},
568
mrreviewer = {P. Abellanas}
569
}
570
571
@Article{ cassels:diophantinecurve,
572
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
573
title = {Diophantine equations with special reference to elliptic
574
curves},
575
journal = {J. London Math. Soc.},
576
volume = {41},
577
year = {1966},
578
pages = {193--291}
579
}
580
581
@InCollection{ cassels:global,
582
author = {Cassels, J.\thinspace{}W.\thinspace{}S.},
583
title = {Global fields},
584
booktitle = {Algebraic Number Theory (Proc. Instructional Conf.,
585
Brighton, 1965)},
586
pages = {42--84},
587
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title = {{Constructing Elements in Shafarevich-Tate Groups of
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title = {Comparison of integral structures on spaces of modular
1174
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title = {Erratum and addendum: ``{T}he role of {S}erre's conjecture
1198
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@Article{ edixhoven:minimal,
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title = {Le r\^{o}le de la conjecture de {S}erre dans la
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title = {Empirical evidence for the {B}irch and {S}winnerton-{D}yer
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author = {Gonz{\'a}lez, J. and Lario, J.-C.},
1728
title = {{$\mathbf{Q}$}-curves and their {M}anin ideals},
1729
journal = {Amer. J. Math.},
1730
fjournal = {American Journal of Mathematics},
1731
volume = {123},
1732
year = {2001},
1733
number = {3},
1734
pages = {475--503},
1735
issn = {0002-9327},
1736
coden = {AJMAAN},
1737
mrclass = {11G05 (11G18)},
1738
mrnumber = {2002e:11070},
1739
mrreviewer = {Ivica Gusi{\'c}}
1740
}
1741
1742
@Article{ gordon-ono:vis,
1743
title = {Modular form {C}ongruences and {S}elmer groups},
1744
author = {McGraw, W.\thinspace{}J. and Ono, K.},
1745
journal = {preprint},
1746
year = {2002}
1747
}
1748
1749
@InCollection{ gouvea-mazur:density,
1750
author = {Gouv\^{e}a, F.\thinspace{}Q. and Mazur, B.},
1751
title = {On the density of modular representations},
1752
booktitle = {Computational perspectives on number theory (Chicago, IL,
1753
1995)},
1754
pages = {127--142},
1755
publisher = {Amer. Math. Soc.},
1756
address = {Providence, RI},
1757
year = {1998},
1758
mrclass = {11F33 (11F80)},
1759
mrnumber = {99a:11056},
1760
mrreviewer = {Andrea Mori}
1761
}
1762
1763
@Article{ gouvea-mazur:families,
1764
author = {Gouv\^ea, F. and Mazur, B.},
1765
title = {Families of modular eigenforms},
1766
journal = {Math. Comp.},
1767
fjournal = {Mathematics of Computation},
1768
volume = {58},
1769
year = {1992},
1770
number = {198},
1771
pages = {793--805},
1772
issn = {0025-5718},
1773
coden = {MCMPAF},
1774
mrclass = {11F33 (11Y35 14G20)},
1775
mrnumber = {93d:11049},
1776
mrrevr = {Bas Edixhoven}
1777
}
1778
1779
@Article{ gouvea:ordinary,
1780
author = {Gouv\^ea, F.\thinspace{}Q.},
1781
title = {On the ordinary {H}ecke algebra},
1782
journal = {J. Number Theory},
1783
fjournal = {Journal of Number Theory},
1784
volume = {41},
1785
year = {1992},
1786
number = {2},
1787
pages = {178--198},
1788
issn = {0022-314X},
1789
coden = {JNUTA9}
1790
}
1791
1792
@Book{ gouvea:slnm,
1793
author = {Gouv\^{e}a, F.\thinspace{}Q.},
1794
title = {Arithmetic of $p$-adic modular forms},
1795
publisher = {Springer-Verlag},
1796
address = {Berlin},
1797
year = {1988},
1798
pages = {viii+121},
1799
isbn = {3-540-18946-7},
1800
mrclass = {11F85 (11F80)},
1801
mrnumber = {91e:11056},
1802
mrreviewer = {Alexey A. Panchishkin}
1803
}
1804
1805
@Book{ greenberg-harper,
1806
author = {Greenberg, M.\thinspace{}J. and Harper, J.\thinspace{}R.},
1807
title = {Algebraic topology},
1808
note = {A first course},
1809
publisher = {Benjamin/Cummings Publishing Co. Inc. Advanced Book
1810
Program},
1811
address = {Reading, Mass.},
1812
year = {1981},
1813
pages = {xi+311 pp. (loose errata)},
1814
isbn = {0-8053-3558-7; 0-8053-3557-9},
1815
mrclass = {55-01},
1816
mrnumber = {83b:55001},
1817
mrrevr = {J. P. May}
1818
}
1819
1820
@Article{ gross-kohnen-zagier,
1821
author = {Gross, B. and Kohnen, W. and Zagier, D.},
1822
title = {Heegner points and derivatives of ${L}$-series. {I}{I}},
1823
journal = {Math. Ann.},
1824
fjournal = {Mathematische Annalen},
1825
volume = {278},
1826
year = {1987},
1827
number = {1-4},
1828
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1829
issn = {0025-5831},
1830
coden = {MAANA3},
1831
mrclass = {11G40 (11F30 11G05 11R29 14G10)},
1832
mrnumber = {89i:11069},
1833
mrrevr = {Lawrence Washington}
1834
}
1835
1836
@Article{ gross-zagier,
1837
author = {Gross, B. and Zagier, D.},
1838
title = {Heegner points and derivatives of \protect{${L}$}-series},
1839
journal = {Invent. Math.},
1840
fjournal = {Inventiones Mathematicae},
1841
volume = {84},
1842
year = {1986},
1843
number = {2},
1844
pages = {225--320},
1845
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1846
coden = {INVMBH},
1847
mrclass = {11G40 (11F11 11G05 14G10)},
1848
mrnumber = {87j:11057},
1849
mrrevr = {Loren D. Olson}
1850
}
1851
1852
@InCollection{ gross:central,
1853
author = {Gross, B.\thinspace{}H.},
1854
title = {${L}$-functions at the central critical point},
1855
booktitle = {Motives (Seattle, WA, 1991)},
1856
pages = {527--535},
1857
publisher = {Amer. Math. Soc.},
1858
address = {Providence, RI},
1859
year = {1994},
1860
mrclass = {11G40 (14G10)},
1861
mrnumber = {95a:11060},
1862
mrrevr = {Jan Nekov{\'a}{\v{r}}}
1863
}
1864
1865
@InCollection{ gross:kolyvagin,
1866
author = {Gross, B.\thinspace{}H.},
1867
title = {Kolyvagin's work on modular elliptic curves},
1868
booktitle = {$L$-functions and arithmetic (Durham, 1989)},
1869
pages = {235--256},
1870
publisher = {Cambridge Univ. Press},
1871
address = {Cambridge},
1872
year = {1991}
1873
}
1874
1875
@Article{ gross:tameness,
1876
author = {Gross, B.\thinspace{}H.},
1877
title = {A tameness criterion for \protect{G}alois representations
1878
associated to modular forms (mod \protect{$p$})},
1879
journal = {Duke Math. J.},
1880
fjournal = {Duke Mathematical Journal},
1881
volume = {61},
1882
year = {1990},
1883
number = {2},
1884
pages = {445--517},
1885
issn = {0012-7094},
1886
coden = {DUMJAO}
1887
}
1888
1889
@Article{ gross_kudla,
1890
author = {Gross, B.\thinspace{}H. and Kudla, S.\thinspace{}S.},
1891
title = {Heights and the central critical values of triple product
1892
{$L$}-functions},
1893
journal = {Compositio Math.},
1894
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1895
volume = {81},
1896
year = {1992},
1897
number = {2},
1898
pages = {143--209},
1899
issn = {0010-437X},
1900
coden = {CMPMAF},
1901
mrclass = {11F66 (11F67 11G40 19F27)},
1902
mrnumber = {93g:11047},
1903
mrreviewer = {Alexey A. Panchishkin}
1904
}
1905
1906
@InCollection{ grothendieck:brauer1,
1907
author = {Grothendieck, Alexander},
1908
title = {Le groupe de {B}rauer. {I}. {A}lg\`ebres d'{A}zumaya et
1909
interpr\'etations diverses},
1910
booktitle = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
1911
pages = {46--66},
1912
publisher = {North-Holland},
1913
address = {Amsterdam},
1914
year = {1968},
1915
mrclass = {14.55},
1916
mrnumber = {39 #5586a}
1917
}
1918
1919
@InCollection{ grothendieck:brauer2,
1920
author = {Grothendieck, Alexander},
1921
title = {Le groupe de {B}rauer. {I}{I}. {T}h\'eorie cohomologique},
1922
booktitle = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
1923
pages = {67--87},
1924
publisher = {North-Holland},
1925
address = {Amsterdam},
1926
year = {1968},
1927
mrclass = {14.55},
1928
mrnumber = {39 #5586b}
1929
}
1930
1931
@InCollection{ grothendieck:brauer3,
1932
author = {Grothendieck, Alexander},
1933
title = {Le groupe de {B}rauer. {I}{I}{I}. {E}xemples et
1934
compl\'ements},
1935
booktitle = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
1936
pages = {88--188},
1937
publisher = {North-Holland},
1938
address = {Amsterdam},
1939
year = {1968},
1940
mrclass = {14.55},
1941
mrnumber = {39 #5586c},
1942
mrrevr = {J. S. Milne}
1943
}
1944
1945
@Book{ grothendieck:monodromie,
1946
author = {Grothendieck, A.},
1947
title = {Groupes de monodromie en g\'eom\'etrie alg\'ebrique.
1948
\protect{I}},
1949
note = {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie
1950
1967--1969 (SGA 7 I), Dirig\'e par A. Grothendieck. Avec la
1951
collaboration de M. Raynaud et D. S. Rim, Lecture Notes in
1952
Mathematics, Vol. 288},
1953
publisher = {Springer-Verlag},
1954
address = {Berlin},
1955
year = {1972},
1956
pages = {viii+523}
1957
}
1958
1959
@InCollection{ gruenberg,
1960
author = {Gruenberg, K.},
1961
title = {Profinite groups},
1962
booktitle = {Algebraic Number Theory (Proc. Instructional Conf.,
1963
Brighton, 1965)},
1964
pages = {116--127},
1965
publisher = {Thompson, Washington, D.C.},
1966
year = {1967}
1967
}
1968
1969
@Article{ guerzhoy:kummer,
1970
title = {Searching for {K}ummer congruences in an infinite slope
1971
family},
1972
author = {Guerzhoy, P.},
1973
year = {2000},
1974
journal = {Preprint}
1975
}
1976
1977
@Book{ guy:unsolved,
1978
author = {Guy, R.\thinspace{}K.},
1979
title = {Unsolved problems in number theory},
1980
edition = {Second},
1981
note = {Unsolved Problems in Intuitive Mathematics, I},
1982
publisher = {Springer-Verlag},
1983
address = {New York},
1984
year = {1994},
1985
pages = {xvi+285},
1986
isbn = {0-387-94289-0},
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mrclass = {11-01 (00A07 11-02)},
1988
mrnumber = {96e:11002},
1989
mrreviewer = {B. M. M. de Weger}
1990
}
1991
1992
@Book{ haberland,
1993
author = {Haberland, Klaus},
1994
title = {Galois cohomology of algebraic number fields},
1995
note = {With two appendices by Helmut Koch and Thomas Zink},
1996
publisher = {VEB Deutscher Verlag der Wissenschaften},
1997
address = {Berlin},
1998
year = {1978},
1999
pages = {145},
2000
mrclass = {12A60},
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mrnumber = {81i:12009},
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mrrevr = {Chih-Han Sah}
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}
2004
2005
@Book{ halmos:naive,
2006
author = {Halmos, Paul R.},
2007
title = {Naive set theory},
2008
series = {The University Series in Undergraduate Mathematics},
2009
publisher = {D. Van Nostrand Co., Princeton, N.J.-Toronto-London-New
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York},
2011
year = {1960},
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pages = {vii+104},
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mrclass = {04.00},
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mrnumber = {22 \#5575},
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mrreviewer = {L. Rieger}
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2018
@Article{ hardy_littlewood:conjf,
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author = {Hardy, G.\thinspace{}H. and Littlewood, J.\thinspace{}E.},
2020
title = {Some {P}roblems of `{P}artitio {N}umerorum.' {I}{I}{I}.
2021
{O}n the {E}xpression of a {N}umber as a {S}um of
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{P}rimes.},
2023
journal = {Acta. Math.},
2024
volume = {44},
2025
year = {1922},
2026
pages = {1--70}
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}
2028
2029
@Book{ hartshorne,
2030
author = {Hartshorne, R.},
2031
title = {Algebraic {G}eometry},
2032
note = {Graduate Texts in Mathematics, No. 52},
2033
publisher = {Springer-Verlag},
2034
address = {New York},
2035
year = {1977},
2036
pages = {xvi+496},
2037
isbn = {0-387-90244-9}
2038
}
2039
2040
@Article{ hatada:eigenvalues79,
2041
author = {Hatada, K.},
2042
title = {Eigenvalues of {H}ecke operators on \protect{${\rm
2043
{S}{L}}(2,\,{\bf {Z}})$}},
2044
journal = {Math. Ann.},
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volume = {239},
2047
year = {1979},
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number = {1},
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pages = {75--96},
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issn = {0025-5831},
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coden = {MAANA3},
2052
mrclass = {10D15},
2053
mrnumber = {80b:10037},
2054
mrreviewer = {Roy Fuller}
2055
}
2056
2057
@Article{ hatada:general,
2058
author = {Hatada, K.},
2059
title = {On classical and {$l$}-adic modular forms of levels
2060
{$Nl\sp m$} and {$N$}},
2061
journal = {J. Number Theory},
2062
fjournal = {Journal of Number Theory},
2063
volume = {87},
2064
year = {2001},
2065
number = {1},
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pages = {1--14},
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coden = {JNUTA9},
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2070
mrnumber = {2002e:11054},
2071
mrreviewer = {Luis V. Dieulefait}
2072
}
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2074
@Article{ hatada:rationality,
2075
author = {Hatada, K.},
2076
title = {Multiplicity one theorem and modular symbols},
2077
journal = {J. Math. Soc. Japan},
2078
fjournal = {Journal of the Mathematical Society of Japan},
2079
volume = {33},
2080
year = {1981},
2081
number = {3},
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pages = {445--470},
2083
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coden = {NISUBC},
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mrclass = {10D12 (12A65)},
2086
mrnumber = {83d:10030},
2087
mrrevr = {Wen Ch'ing Winnie Li}
2088
}
2089
2090
@Book{ hellegouarch:invitation,
2091
author = {Hellegouarch, Y.},
2092
title = {Invitation aux math\'ematiques de {F}ermat-{W}iles},
2093
publisher = {Masson},
2094
address = {Paris},
2095
year = {1997},
2096
pages = {viii+401},
2097
isbn = {2-225-83008-8},
2098
mrclass = {11-01 (11D41 11F11 11G05 11G18)},
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mrnumber = {99e:11001},
2100
mrrevr = {Massimo Bertolini}
2101
}
2102
2103
@Article{ hida:invent86,
2104
author = {Hida, H.},
2105
title = {Galois representations into \protect{${\rm {G}{L}}\sb
2106
2({\bf {Z}}\sb p[[{X}]])$} attached to ordinary cusp forms},
2107
journal = {Invent. Math.},
2108
fjournal = {Inventiones Mathematicae},
2109
volume = {85},
2110
year = {1986},
2111
number = {3},
2112
pages = {545--613},
2113
issn = {0020-9910},
2114
coden = {INVMBH},
2115
mrclass = {11F11 (11F33 11F85 11R23)},
2116
mrnumber = {87k:11049},
2117
mrrevr = {Ernst-Wilhelm Zink}
2118
}
2119
2120
@Article{ hida:iwasawa,
2121
author = {Hida, H.},
2122
title = {Iwasawa modules attached to congruences of cusp forms},
2123
journal = {Ann. Sci. \'Ecole Norm. Sup. (4)},
2124
fjournal = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
2125
Quatri\`eme S\'erie},
2126
volume = {19},
2127
year = {1986},
2128
number = {2},
2129
pages = {231--273},
2130
issn = {0012-9593},
2131
coden = {ASENAH},
2132
mrclass = {11F33 (11G18 11R23)},
2133
mrnumber = {88i:11023},
2134
mrrevr = {Yasutaka Ihara}
2135
}
2136
2137
@Article{ hida:modularity,
2138
author = {Hida, H.},
2139
title = {Modularity {P}roblems of {$\Q$}-{M}otives and
2140
{B}ase-{C}hange},
2141
journal = {Preprint, {\tt http://www.math.ucla.edu/~hida/}},
2142
year = {2000}
2143
}
2144
2145
@Article{ hijikata:trace,
2146
author = {Hijikata, H.},
2147
title = {Explicit formula of the traces of \protect{H}ecke
2148
operators for \protect{$\Gamma_0(N)$}},
2149
journal = {J. Math. Soc. Japan},
2150
number = {1},
2151
volume = {26},
2152
year = {1974},
2153
pages = {56--82}
2154
}
2155
2156
@Book{ hindry-silverman:diophantine,
2157
author = {Hindry, Marc and Silverman, Joseph H.},
2158
title = {Diophantine geometry},
2159
note = {An introduction},
2160
publisher = {Springer-Verlag},
2161
address = {New York},
2162
year = {2000},
2163
pages = {xiv+558},
2164
isbn = {0-387-98975-7; 0-387-98981-1},
2165
mrclass = {11Gxx (11-02 11G10 11G30 11G50 14G25)},
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mrnumber = {2001e:11058},
2167
mrreviewer = {Dino J. Lorenzini}
2168
}
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2170
@InProceedings{ hpf,
2171
author = {Swinnerton-Dyer, H.\thinspace{}P.\thinspace{}F.},
2172
title = {On $\ell$-adic representations and congruences for
2173
coefficients of modular forms},
2174
booktitle = {Proceedings of the International Summer School, University
2175
of Antwerp, RUCA, July 17--August 3, 1972},
2176
pages = {1--55. Lecture Notes in Math., Vol. 350},
2177
publisher = {Springer},
2178
address = {Berlin},
2179
year = {1973}
2180
}
2181
2182
@Article{ igusa:fibre,
2183
author = {Igusa, J.},
2184
title = {Fibre systems of \protect{J}acobian varieties},
2185
journal = {Amer. J. Math.},
2186
volume = {78},
2187
year = {1956},
2188
pages = {171--199}
2189
}
2190
2191
@Book{ jacquet-langlands,
2192
author = {Jacquet, H. and Langlands, R.\thinspace{}P.},
2193
title = {Automorphic forms on \protect{${\rm {G}{L}}(2)$}},
2194
note = {Lecture Notes in Mathematics, Vol. 114},
2195
publisher = {Springer-Verlag},
2196
address = {Berlin},
2197
year = {1970},
2198
pages = {vii+548}
2199
}
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2201
@Article{ jarvis:hilbert,
2202
author = {Jarvis, F.},
2203
title = {On \protect{G}alois representations associated to
2204
\protect{H}ilbert modular forms},
2205
journal = {J. Reine Angew. Math.},
2206
fjournal = {Journal f\"ur die Reine und Angewandte Mathematik},
2207
volume = {491},
2208
year = {1997},
2209
pages = {199--216},
2210
issn = {0075-4102},
2211
coden = {JRMAA8}
2212
}
2213
2214
@Article{ jarvis:level,
2215
author = {Jarvis, F.},
2216
title = {Level lowering for modular mod \protect{$\ell$}
2217
representations over totally real fields\-},
2218
journal = {Math. Ann.},
2219
fjournal = {Mathematische Annalen},
2220
volume = {313},
2221
year = {1999},
2222
number = {1},
2223
pages = {141--160},
2224
issn = {0025-5831},
2225
coden = {MAANA}
2226
}
2227
2228
@Article{ jarvis:mazur,
2229
author = {Jarvis, F.},
2230
title = {Mazur's principle for totally real fields of odd degree},
2231
journal = {Compositio Math.},
2232
fjournal = {Compositio Mathematica},
2233
volume = {116},
2234
year = {1999},
2235
number = {1},
2236
pages = {39--79},
2237
issn = {0010-437X},
2238
coden = {CMPMAF}
2239
}
2240
2241
@InCollection{ jochnowitz:conjecture,
2242
author = {Jochnowitz, N.},
2243
title = {A $p$-adic conjecture about derivatives of ${L}$-series
2244
attached to modular forms},
2245
booktitle = {$p$-adic monodromy and the {B}irch and {S}winnerton-{D}yer
2246
conjecture},
2247
pages = {239--263},
2248
publisher = {Amer. Math. Soc.},
2249
address = {Providence, RI},
2250
year = {1994},
2251
mrclass = {11F33 (11F67 11F85 11G40)},
2252
mrnumber = {95g:11037},
2253
mrrevr = {Andrea Mori}
2254
}
2255
2256
@Article{ jochnowitz:duke,
2257
author = {Jochnowitz, N.},
2258
title = {The index of the {H}ecke ring, ${T}\sb{k}$, in the ring of
2259
integers of \protect{${T}\sb{k}\otimes {\bf {Q}}$}},
2260
journal = {Duke Math. J.},
2261
fjournal = {Duke Mathematical Journal},
2262
volume = {46},
2263
year = {1979},
2264
number = {4},
2265
pages = {861--869},
2266
issn = {0012-7094},
2267
coden = {DUMJAO},
2268
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2269
mrnumber = {80k:10023},
2270
mrrevr = {Henri Cohen}
2271
}
2272
2273
@Article{ jochnowitz:local,
2274
author = {Jochnowitz, N.},
2275
title = {A study of the local components of the \protect{H}ecke
2276
algebra mod \protect{$\ell$}},
2277
journal = {Trans. Amer. Math. Soc.},
2278
fjournal = {Transactions of the American Mathematical Society},
2279
volume = {270},
2280
year = {1982},
2281
number = {1},
2282
pages = {253--267},
2283
issn = {0002-9947},
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@Article{ jones:thesis,
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@Article{ jordan-livne:epsilon,
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author = {Jordan, B.\thinspace{}W. and Livn{\'e}, R.},
2297
title = {Conjecture ``epsilon'' for weight \protect{$k>2$}},
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journal = {Bull. Amer. Math. Soc. (N.S.)},
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volume = {21},
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@Article{ jordan-livne:sha,
2309
author = {Jordan, B.\thinspace{}W. and Livn{\'e}, R.},
2310
title = {On {A}tkin-{L}ehner quotients of {S}himura curves},
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journal = {Bull. London Math. Soc.},
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@Article{ joshi,
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journal = {Internat. Math. Res. Notices},
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@InProceedings{ jps,
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author = {Serre, J-P.},
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title = {Congruences et formes modulaires [d'apr\`es
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2348
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@Article{ kato:secret,
2350
author = {Kato, K.},
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title = {$p$-adic {H}odge theory and values of zeta functions of
2352
modular forms},
2353
journal = {Preprint},
2354
pages = {244 pages}
2355
}
2356
2357
@Article{ katz:annals75,
2358
author = {Katz, N.\thinspace{}M.},
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title = {Higher congruences between modular forms},
2360
journal = {Ann. of Math. (2)},
2361
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year = {1975},
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2367
}
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@InProceedings{ katz:antwerp350,
2370
author = {Katz, N.\thinspace{}M.},
2371
title = {$p$-adic properties of modular schemes and modular forms},
2372
booktitle = {Modular functions of one variable, III (Proc. Internat.
2373
Summer School, Univ. Antwerp, Antwerp, 1972)},
2374
pages = {69--190. Lecture Notes in Mathematics, Vol. 350},
2375
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2376
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2377
year = {1973}
2378
}
2379
2380
@Article{ katz:torsion,
2381
author = {Katz, N.\thinspace{}M.},
2382
title = {Galois properties of torsion points on abelian varieties},
2383
journal = {Invent. Math.},
2384
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2385
volume = {62},
2386
year = {1981},
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2391
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2393
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2394
}
2395
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@InProceedings{ katzbonn,
2397
author = {Katz, N.\thinspace{}M.},
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title = {A result on modular forms in characteristic $p$},
2399
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pages = {53--61. Lecture Notes in Math., Vol. 601},
2402
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2403
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2404
year = {1977}
2405
}
2406
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@Book{ katzmazur,
2408
author = {Katz, N.\thinspace{}M. and Mazur, B.},
2409
title = {Arithmetic moduli of elliptic curves},
2410
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2411
address = {Princeton, N.J.},
2412
year = {1985},
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2415
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2416
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@Article{ khare:manu,
2418
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2419
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2420
journal = {Manuscripta Math.},
2421
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2428
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2429
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2430
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2431
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2432
2433
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2434
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2435
title = {Modular {V}arieties and {V}isibility},
2436
journal = {Ph.D. thesis, Harvard University},
2437
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2438
}
2439
2440
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2441
author = {Knapp, A.\thinspace{}W.},
2442
title = {Elliptic curves},
2443
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2444
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2445
year = {1992},
2446
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2447
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2448
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2449
2450
@Book{ koblitz:cong,
2451
author = {Koblitz, N.},
2452
title = {Introduction to elliptic curves and modular forms},
2453
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2454
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2455
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2456
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2457
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2458
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2459
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2460
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2461
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2462
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2463
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2464
2465
@InProceedings{ kohel-stein:ants4,
2466
author = "Kohel, D.\thinspace{}R. and Stein, W.\thinspace{}A.",
2467
title = "Component {G}roups of {Q}uotients of \protect{$J_0(N)$}",
2468
booktitle = {Proceedings of the 4th International Symposium (ANTS-IV),
2469
Leiden, Netherlands, July 2--7, 2000},
2470
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2471
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2472
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2473
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2474
2475
@Article{ kohel:computing,
2476
author = "Kohel, D.\thinspace{}R.",
2477
title = "Computing modular curves via quaternions",
2478
journal = "Fourth CANT Conference",
2479
year = 1997
2480
}
2481
2482
@Article{ kohel:hecke,
2483
author = "Kohel, D.\thinspace{}R.",
2484
title = "Hecke Module Structure of Quaternions",
2485
journal = "In K. Miyake, ed., {\em Class Field Theory -- Its
2486
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2487
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2488
}
2489
2490
@Article{ koike:conjtwist,
2491
author = "Koike, M.",
2492
title = "On certain abelian varieties obtained from new forms of
2493
weight $2$ on \protect{$\Gamma_0(3^4)$ and
2494
$\Gamma_0(3^5)$}",
2495
journal = {Nogoya Math. J.},
2496
volume = {62},
2497
year = {1976},
2498
pages = {29--39}
2499
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2500
2501
@Article{ kolyvagin-logachev:finiteness,
2502
author = {Kolyvagin, V.\thinspace{}A. and Logachev, D.\thinspace{}Y.},
2503
title = {Finiteness of the \protect{S}hafarevich-\protect{T}ate
2504
group and the group of rational points for some modular
2505
abelian varieties},
2506
journal = {Algebra i Analiz},
2507
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2508
volume = {1},
2509
year = {1989},
2510
number = {5},
2511
pages = {171--196},
2512
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2513
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2514
2515
@Article{ kolyvagin-logachev:totallyreal,
2516
author = "Kolyvagin, V.\thinspace{}A. and Logachev,
2517
D.\thinspace{}Y.",
2518
title = "Finiteness of \protect{$\Sha$} over totally real fields",
2519
journal = {Math. USSR Izvestiya},
2520
volume = {39},
2521
year = {1992},
2522
number = {1},
2523
pages = {829--853}
2524
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2525
2526
@InCollection{ kolyvagin:euler_systems,
2527
author = {Kolyvagin, V. A.},
2528
title = {Euler systems},
2529
booktitle = {The Grothendieck Festschrift, Vol.\ II},
2530
pages = {435--483},
2531
publisher = {Birkh\"auser Boston},
2532
address = {Boston, MA},
2533
year = {1990},
2534
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2535
mrnumber = {92g:11109},
2536
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2537
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2538
2539
@InProceedings{ kolyvagin:mordellweil,
2540
author = {Kolyvagin, V.\thinspace{}A.},
2541
title = {On the {M}ordell-{W}eil group and the {S}hafarevich-{T}ate
2542
group of modular elliptic curves},
2543
booktitle = {Proceedings of the International Congress of
2544
Mathematicians, Vol.\ I, II (Kyoto, 1990)},
2545
pages = {429--436},
2546
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2547
address = {Tokyo},
2548
year = {1991},
2549
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2550
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2551
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2552
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2553
2554
@Article{ kolyvagin:structure_of_selmer,
2555
author = {Kolyvagin, V. A.},
2556
title = {On the structure of {S}elmer groups},
2557
journal = {Math. Ann.},
2558
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2559
volume = {291},
2560
year = {1991},
2561
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2562
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2563
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2565
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2566
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2567
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2568
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2569
2570
@InCollection{ kolyvagin:structureofsha,
2571
author = {Kolyvagin, V.\thinspace{}A.},
2572
title = {On the structure of {S}hafarevich-{T}ate groups},
2573
booktitle = {Algebraic geometry (Chicago, IL, 1989)},
2574
pages = {94--121},
2575
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2576
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2577
year = {1991}
2578
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2579
2580
@Article{ kolyvagin:subclass,
2581
author = {Kolyvagin, V. A.},
2582
title = {Finiteness of ${E}({\bf {Q}})$ and {S}{H}$({E},{\bf {Q}})$
2583
for a subclass of {W}eil curves},
2584
journal = {Izv. Akad. Nauk SSSR Ser. Mat.},
2585
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2586
volume = {52},
2587
year = {1988},
2588
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2589
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2590
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2591
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2592
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2593
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2594
}
2595
2596
@Article{ kolyvagin:weil,
2597
author = {Kolyvagin, V. A.},
2598
title = {The {M}ordell-{W}eil and {S}hafarevich-{T}ate groups for
2599
{W}eil elliptic curves},
2600
journal = {Izv. Akad. Nauk SSSR Ser. Mat.},
2601
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2602
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2603
year = {1988},
2604
number = {6},
2605
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2606
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2609
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2610
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2611
2612
@Article{ kramer:largesha,
2613
author = {Kramer, K.},
2614
title = {A family of semistable elliptic curves with large
2615
{T}ate-{S}hafarevitch groups},
2616
journal = {Proc. Amer. Math. Soc.},
2617
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2618
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2619
year = {1983},
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2626
mrreviewer = {Reinhard B{\"o}lling}
2627
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2628
2629
@Book{ kubert-lang,
2630
author = {Kubert, D.\thinspace{}S. and Lang, S.},
2631
title = {Modular units},
2632
series = {Grundlehren der Mathematischen Wissenschaften [Fundamental
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2634
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2635
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2636
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2637
year = {1981},
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pages = {xiii+358},
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2643
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2646
author = {Lang, S. and Tate, J.},
2647
title = {Principal homogeneous spaces over abelian varieties},
2648
journal = {Amer. J. Math.},
2649
volume = {80},
2650
year = {1958},
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pages = {659--684}
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@Book{ lang:algebra,
2655
author = {Lang, S.},
2656
title = {Algebra},
2657
edition = {Third},
2658
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2659
year = {1993},
2660
pages = {xv+912},
2661
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2664
@Book{ lang:ant,
2665
author = {Lang, S.},
2666
title = {Algebraic number theory},
2667
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2668
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2669
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2670
year = {1994},
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2675
@Article{ lang:finitefields,
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author = {Lang, S.},
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2678
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2679
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2680
year = {1956},
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2684
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2685
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2686
2687
@Book{ lang:modular,
2688
author = {Lang, S.},
2689
title = {Introduction to modular forms},
2690
note = {With appendixes by D. Zagier and W. Feit, Corrected
2691
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2692
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2693
address = {Berlin},
2694
year = {1995},
2695
pages = {x+261},
2696
isbn = {3-540-07833-9}
2697
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2699
@Book{ lang:nt3,
2700
author = {Lang, S.},
2701
title = {Number theory. {I}{I}{I}},
2702
note = {Diophantine geometry},
2703
publisher = {Springer-Verlag},
2704
address = {Berlin},
2705
year = {1991},
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pages = {xiv+296},
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2710
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2711
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2713
@InProceedings{ langlands:antwerp2,
2714
author = {Langlands, R.\thinspace{}P.},
2715
title = {Modular forms and $\ell $-adic representations},
2716
booktitle = {Proceedings of the International Summer School, University
2717
of Antwerp, RUCA, July 17--August 3, 1972},
2718
editor = {Deligne, P. and Kuyk, W.},
2719
pages = {361--500. Lecture Notes in Math., Vol. 349},
2720
publisher = {Springer},
2721
address = {Berlin},
2722
year = {1973},
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2726
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2727
2728
@Book{ langlands:basechange,
2729
author = {Langlands, R.\thinspace{}P.},
2730
title = {Base change for \protect{${\rm {G}{L}}(2)$}},
2731
publisher = {Princeton University Press},
2732
address = {Princeton, N.J.},
2733
year = {1980},
2734
pages = {vii+237},
2735
isbn = {0-691-08263-4; 0-691-08272-3}
2736
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2738
@Article{ lenstra-oort:additive,
2739
author = {Lenstra, Jr., H. W. and Oort, F.},
2740
title = {Abelian varieties having purely additive reduction},
2741
journal = {J. Pure Appl. Algebra},
2742
fjournal = {Journal of Pure and Applied Algebra},
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volume = {36},
2744
year = {1985},
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pages = {281--298},
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coden = {JPAAA2},
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mrclass = {14K15 (11G10 14G20)},
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mrnumber = {86e:14020},
2751
mrreviewer = {Joseph H. Silverman}
2752
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2753
2754
@InCollection{ lenstra-smit:explicit,
2755
author = {de Smit, B. and Lenstra, H.\thinspace{}W.,Jr.},
2756
title = {Explicit construction of universal deformation rings},
2757
booktitle = {Modular forms and \protect{F}ermat's last theorem (Boston,
2758
MA, 1995)},
2759
pages = {313--326},
2760
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2761
address = {New York},
2762
year = {1997}
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}
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2765
@Book{ lenstras:nfs,
2766
title = {The development of the number field sieve},
2767
editor = {Lenstra, A.\thinspace{}K. and Lenstra, Jr.,
2768
H.\thinspace{}W.},
2769
publisher = {Springer-Verlag},
2770
address = {Berlin},
2771
year = {1993},
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pages = {viii+131},
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2779
@Article{ lichtenbaum:curves,
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author = {Lichtenbaum, Stephen},
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2782
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year = {1968},
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pages = {380--405},
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@Article{ lichtenbaum:duality,
2792
author = {Lichtenbaum, S.},
2793
title = {Duality theorems for curves over \protect{$p$}-adic
2794
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2795
journal = {Invent. Math.},
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volume = {7},
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year = {1969},
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pages = {120--136}
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@Article{ lidia,
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title = {\protect{LiDIA: C++} number theory library},
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author = {Buchmann, J.}
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2806
@Article{ livne:conductors,
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author = {Livn{\'e}, R.},
2808
title = {On the conductors of mod \protect{$\ell$} \protect{G}alois
2809
representations coming from modular forms},
2810
journal = {J. Number Theory},
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year = {1989},
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2820
@Proceedings{ lms254,
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title = {Galois Representations in Arithmetic Algebraic Geometry},
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booktitle = {Galois Representations in Arithmetic Algebraic Geometry},
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editor = {Scholl A.\thinspace{}J. and Taylor R.\thinspace{}L.},
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pages = {493},
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year = {1998},
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@Article{ lorenzini:abvarred,
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author = {Lorenzini, D.\thinspace{}J.},
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title = "On the Jacobian of the Modular Curve \protect{$X_0(N)$}",
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journal = "preprint"
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2835
@Article{ lorenzini:compgrp,
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author = {Lorenzini, D.\thinspace{}J.},
2837
title = {On the group of components of a \protect{N}\'eron model},
2838
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