@article{agashe, author="Agash\'{e}, A.", title="On invisible elements of the \protect{Tate-Shafarevich} group", year=1999, pages={369--374}, journal="Th\'{e}orie des nombres", volume={328} } @book {antwerpiv, TITLE = {Modular functions of one variable. \protect{IV}}, BOOKTITLE = {Proceedings of the International Summer School on Modular Functions of One Variable and Arithmetical Applications, RUCA, University of Antwerp, Antwerp, July 17--August 3, 1972}, EDITOR = {Birch, B. J. and Kuyk, W.}, NOTE = {Lecture Notes in Mathematics, Vol. 476}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1975}, PAGES = {iv+151}, } @incollection{birch:bsd, AUTHOR = {Birch, B.J.}, TITLE = {Elliptic curves over \protect{${\mathbf{Q}}$: {A}} progress report}, BOOKTITLE = {1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969)}, PAGES = {396--400}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, R.I.}, YEAR = {1971} } @article {boston-lenstra-ribet, AUTHOR = {Boston, N. and Lenstra, H.W., Jr. and Ribet, K.A.}, TITLE = {Quotients of group rings arising from two-dimensional representations}, JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.}, FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, VOLUME = {312}, YEAR = {1991}, NUMBER = {4}, PAGES = {323--328}, ISSN = {0764-4442}, CODEN = {CASMEI}, } @book{buhler-thesis, AUTHOR = {Buhler, Joe P.}, TITLE = {Icosahedral \protect{G}alois representations}, NOTE = {Lecture Notes in Mathematics, Vol. 654}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1978}, PAGES = {ii+143}, ISBN = {3-540-08844-X}, } @article{atkin-lehner, AUTHOR = {Atkin, A. O. L. and Lehner, J.}, TITLE = {Hecke operators on \protect{$\Gamma \sb{0}(m)$}}, JOURNAL = {Math. Ann.}, VOLUME = {185}, YEAR = {1970}, PAGES = {134--160}, } @article{brueggeman:nonexistence, author = {Brueggeman, S.}, title = {The non-existence of certain \protect{Galois} extensions unramified outside 5}, journal = {Journal of Number Theory}, volume = {75}, date = {1999}, pages = {47--52} } @article{brumer:rank, AUTHOR = {Brumer, A.}, TITLE = {The rank of \protect{${J}\sb 0({N})$}}, NOTE = {Columbia University Number Theory Seminar (New York, 1992)}, JOURNAL = {Ast\'erisque}, FJOURNAL = {Ast\'erisque}, NUMBER = {228}, YEAR = {1995}, PAGES = {3, 41--68}, ISSN = {0303-1179}, } @incollection {cassels:global, AUTHOR = {Cassels, J. W. S.}, TITLE = {Global fields}, BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965)}, PAGES = {42--84}, PUBLISHER = {Thompson, Washington, D.C.}, YEAR = {1967}, } @article{CAREARLY, author="Carayol, H.", title={Sur les \protect{repr\'esentations} \protect{$\ell$-adiques} \protect{associ\'ees} aux formes modulaires de \protect{Hilbert}}, journal={Ann. scient. \protect{\'Ec.} Norm. Sup., \protect{$4^{\rm eb}$ s\'erie}}, volume={19}, year={1986}, pages={409--468} } @article{CAR, author={Carayol, H.}, title={Sur les \protect{repr\'esentations} galoisiennes modulo \protect{$\ell$ attach\'ees} aux formes modulaires}, journal={Duke Math. J.}, volume={59}, year ={1989}, pages ={785--801} } @article{coleman:monodromy, author = {Coleman, R.}, title = {The monodromy pairing}, journal = {Asian Math. Journal}, year = {1999} } @book {cremona:algs, AUTHOR = {Cremona, J.E.}, TITLE = {Algorithms for modular elliptic curves}, EDITION = {Second}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1997}, PAGES = {vi+376}, ISBN = {0-521-59820-6}, } @article{cremona:gammaone, AUTHOR = {Cremona, J.E.}, TITLE = {Modular symbols for \protect{$\Gamma\sb 1({N})$} and elliptic curves with everywhere good reduction}, JOURNAL = {Math. Proc. Cambridge Philos. Soc.}, FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical Society}, VOLUME = {111}, YEAR = {1992}, NUMBER = {2}, PAGES = {199--218}, ISSN = {0305-0041}, CODEN = {MPCPCO}, } @article{cremona-mazur, author="J.E. Cremona and B. Mazur", title="Visualizing elements in the \protect{Shafarevich-Tate} Group", journal="Proceedings of the Arizona Winter School", year=1998, } @book {curtis-reiner, AUTHOR = {Curtis, C.W. and Reiner, I.}, TITLE = {Representation theory of finite groups and associative algebras}, NOTE = {Pure and Applied Mathematics, Vol. XI}, PUBLISHER = {Interscience Publishers, a division of John Wiley \& Sons, New York-London}, YEAR = {1962}, PAGES = {xiv+685}, } @incollection{ddt, AUTHOR = {Darmon, H. and Diamond, F. and Taylor, R.}, TITLE = {Fermat's last theorem}, BOOKTITLE = {Current developments in mathematics, 1995 (Cambridge, MA)}, PAGES = {1--154}, PUBLISHER = {Internat. Press}, ADDRESS = {Cambridge, MA}, YEAR = {1994}, } @inproceedings {deligne-rapoport, AUTHOR = {Deligne, P. and Rapoport, M.}, TITLE = {Les sch\'emas de modules de courbes elliptiques}, BOOKTITLE = {Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)}, PAGES = {143--316. Lecture Notes in Math., Vol. 349}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1973}, } @article {diamond-kramer, AUTHOR = {Diamond, F. and Kramer, K.}, TITLE = {Modularity of a family of elliptic curves}, JOURNAL = {Math. Res. Lett.}, FJOURNAL = {Mathematical Research Letters}, VOLUME = {2}, YEAR = {1995}, NUMBER = {3}, PAGES = {299--304}, ISSN = {1073-2780}, } @article{hijikata:trace, author={Hijikata, H.}, title={Explicit formula of the traces of \protect{H}ecke operators for \protect{$\Gamma_0(N)$}}, volume={26}, year={1974}, pages={56--82} } @book {katzmazur, AUTHOR = {Katz, N.M. and Mazur, B.}, TITLE = {Arithmetic moduli of elliptic curves}, PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, N.J.}, YEAR = {1985}, PAGES = {xiv+514}, ISBN = {0-691-08349-5, 0-691-08352-5}, } @incollection {lenstra-smit:explicit, AUTHOR = {de Smit, B. and Lenstra, H.W.,Jr.}, TITLE = {Explicit construction of universal deformation rings}, BOOKTITLE = {Modular forms and Fermat's last theorem (Boston, MA, 1995)}, PAGES = {313--326}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {1997}, } @incollection {mazur:deforming, AUTHOR = {Mazur, B.}, TITLE = {Deforming \protect{G}alois representations}, BOOKTITLE = {Galois groups over \protect{${\bf Q}$} (Berkeley, CA, 1987)}, PAGES = {385--437}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {1989}, } @article {mazur-ribet, AUTHOR = {Mazur, B. and Ribet, K.A.}, TITLE = {Two-dimensional representations in the arithmetic of modular curves}, NOTE = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)}, JOURNAL = {Ast\'erisque}, FJOURNAL = {Ast\'erisque}, NUMBER = {196-197}, YEAR = {1991}, PAGES = {6, 215--255 (1992)}, ISSN = {0303-1179}, } @book {MR89b:14029, TITLE = {Arithmetic geometry}, EDITOR = {Cornell, G. and Silverman, J.H.}, NOTE = {Papers from the conference held at the University of Connecticut, Storrs, Conn., July 30--August 10, 1984}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1986}, PAGES = {xvi+353}, ISBN = {0-387-96311-1}, } @book{milne:duality, author = {Milne, J.S.}, TITLE = {Arithmetic duality theorems}, PUBLISHER = {Academic Press Inc.}, ADDRESS = {Boston, Mass.}, YEAR = {1986}, PAGES = {x+421}, ISBN = {0-12-498040-6}, } @incollection {milne:abvars, AUTHOR = {Milne, J.S.}, TITLE = {Abelian varieties}, BOOKTITLE = {Arithmetic geometry (Storrs, Conn., 1984)}, PAGES = {103--150}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {1986}, } @incollection {rosen:abvars, AUTHOR = {Rosen, M.}, TITLE = {Abelian varieties over \protect{${\bf {C}}$}}, BOOKTITLE = {Arithmetic geometry (Storrs, Conn., 1984)}, PAGES = {79--101}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {1986}, } @article{SAITO, author={T. Saito}, title={\protect{Modular forms and $p$-adic Hodge theory}}, journal={Invent. Math.}, volume={129}, year={1997}, pages={607--620}} @book {shimura:intro, AUTHOR = {Shimura, G.}, TITLE = {Introduction to the arithmetic theory of automorphic functions}, NOTE = {\protect{Kan\^o} Memorial Lectures, No. 1}, PUBLISHER = {Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo}, YEAR = {1971}, PAGES = {xiv+267}, } @article {wiles:fermat, AUTHOR = {Wiles, A.}, TITLE = {Modular elliptic curves and \protect{F}ermat's last theorem}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {141}, YEAR = {1995}, NUMBER = {3}, PAGES = {443--551}, ISSN = {0003-486X}, CODEN = {ANMAAH}, } @article{diamond:modularity, AUTHOR = {Conrad, B. and Diamond, F. and Taylor, R.}, TITLE = {Modularity of certain potentially \protect{B}arsotti-\protect{T}ate {G}alois representations}, JOURNAL = {J. Amer. Math. Soc.}, FJOURNAL = {Journal of the American Mathematical Society}, VOLUME = {12}, YEAR = {1999}, NUMBER = {2}, PAGES = {521--567}, ISSN = {0894-0347}, } @inproceedings{merel:1585, AUTHOR = {Merel, L.}, TITLE = {Universal \protect{F}ourier expansions of modular forms}, BOOKTITLE = {On \protect{A}rtin's conjecture for odd $2$-dimensional representations}, PAGES = {59--94}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1994}, } @article{buzzard-taylor, author={Taylor, R. and Buzzard, K.}, title={Companion forms and weight 1 forms}, year={1999}, } @article{taylor-wiles:fermat, AUTHOR = {Taylor, R. and Wiles, A.}, TITLE = {Ring-theoretic properties of certain \protect{H}ecke algebras}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {141}, YEAR = {1995}, NUMBER = {3}, PAGES = {553--572}, ISSN = {0003-486X}, CODEN = {ANMAAH}, } @article{edixhoven:serre, author={Edixhoven, B.}, title={NOT DONE. \protect{S}erre's conjectures in \protect{B}oston proceedings} } @article{edixhoven:eisen, AUTHOR = {Edixhoven, B.}, TITLE = {L'action de l'alg\`ebre de \protect{H}ecke sur les groupes de composantes des jacobiennes des courbes modulaires est ``{E}isenstein''}, NOTE = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)}, JOURNAL = {Ast\'erisque}, FJOURNAL = {Ast\'erisque}, NUMBER = {196-197}, YEAR = {1991}, PAGES = {7--8, 159--170 (1992)}, ISSN = {0303-1179}, } @article {edixhoven:weight, AUTHOR = {Edixhoven, B.}, TITLE = {The weight in \protect{S}erre's conjectures on modular forms}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {109}, YEAR = {1992}, NUMBER = {3}, PAGES = {563--594}, ISSN = {0020-9910}, CODEN = {INVMBH}, } @article {edixcole, AUTHOR = {Coleman, R.F. and Edixhoven, B.}, TITLE = {On the semi-simplicity of the ${U}\sb p$-operator on modular forms}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {310}, YEAR = {1998}, NUMBER = {1}, PAGES = {119--127}, ISSN = {0025-5831}, CODEN = {MAANA}, } @article {coleman-voloch, AUTHOR = {Coleman, R.F. and Voloch, J.F.}, TITLE = {Companion forms and \protect{K}odaira-\protect{S}pencer theory}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {110}, YEAR = {1992}, NUMBER = {2}, PAGES = {263--281}, ISSN = {0020-9910}, CODEN = {INVMBH}, } @article{empiracalbsd, AUTHOR = {Flynn, E. V. and Lepr\'{e}vost F. and Schaeffer, E. F. and Stoll, M. and Wetherell J. L.}, TITLE = {Empirical Evidence for the Birch and Swinnerton-Dyer Conjectures for Modular Jacobians of Genus 2 Curves}, YEAR = {1999}, JOURNAL = {Preprint} } @inproceedings{frey:boston, AUTHOR = {Frey, G.}, TITLE = {On ternary equations of \protect{F}ermat type and relations with elliptic curves}, BOOKTITLE = {Modular forms and Fermat's last theorem (Boston, MA, 1995)}, PAGES = {527--548}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {1997}, crossref="boston" } @incollection{frey-muller, AUTHOR = {Frey, G. and M{\"u}ller, M.}, TITLE = {Arithmetic of modular curves and applications}, BOOKTITLE = {Algorithmic algebra and number theory (Heidelberg, 1997)}, PAGES = {11--48}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1999} } @incollection {frohlich:local, AUTHOR = {Fr{\"o}hlich, A.}, TITLE = {Local fields}, BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965) }, PAGES = {1--41}, PUBLISHER = {Thompson, Washington, D.C.}, YEAR = {1967}, } @article {gross:tameness, AUTHOR = {Gross, Benedict H.}, TITLE = {A tameness criterion for \protect{G}alois representations associated to modular forms (mod \protect{$p$})}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {61}, YEAR = {1990}, NUMBER = {2}, PAGES = {445--517}, ISSN = {0012-7094}, CODEN = {DUMJAO}, } @book {grothendieck:monodromie, author= {Grothendieck, A.}, TITLE = {Groupes de monodromie en g\'eom\'etrie alg\'ebrique. {I}}, NOTE = {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie 1967--1969 (SGA 7 I), Dirig\'e par A. Grothendieck. Avec la collaboration de M. Raynaud et D. S. Rim, Lecture Notes in Mathematics, Vol. 288}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1972}, PAGES = {viii+523}, } @book {hartshorne, AUTHOR = {Hartshorne, R.}, TITLE = {Algebraic geometry}, NOTE = {Graduate Texts in Mathematics, No. 52}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1977}, PAGES = {xvi+496}, ISBN = {0-387-90244-9}, } @article {igusa:fibre, AUTHOR = {Igusa, J.}, TITLE = {Fibre systems of \protect{J}acobian varieties}, JOURNAL = {Amer. J. Math.}, VOLUME = {78}, YEAR = {1956}, PAGES = {171--199}, } @article {jochnowitz:local, AUTHOR = {Jochnowitz, N.}, TITLE = {A study of the local components of the {H}ecke algebra mod $l$}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {270}, YEAR = {1982}, NUMBER = {1}, PAGES = {253--267}, ISSN = {0002-9947}, CODEN = {TAMTAM}, } @article{kohel:hecke, author="Kohel, D.", title="Hecke Module Structure of Quaternions", year=1998 } @article{koike:conjtwist, author="Koike, M.", title="On certain abelian varieties obtained from new forms of weight $2$ on \protect{$\Gamma_0(3^4)$ and $\Gamma_0(3^5)$}", journal={Nogoya Math. J.}, volume={62}, year={1976}, pages={29--39} } @article{kolyvagin-logachev:totallyreal, author = "Kolyvagin, V.A. and Logachev, D.Y.", title = "Finiteness of \protect{$\Sha$} over totally real fields", journal={Math. USSR Izvestiya}, volume ={39}, year = {1992}, number = {1}, pages={829--853} } @article{kolyvagin-logachev:finiteness, AUTHOR = {Kolyvagin, V.A. and Logachev, D.Y.}, TITLE = {Finiteness of the \protect{S}hafarevich-\protect{T}ate group and the group of rational points for some modular abelian varieties}, JOURNAL = {Algebra i Analiz}, FJOURNAL = {Algebra i Analiz}, VOLUME = {1}, YEAR = {1989}, NUMBER = {5}, PAGES = {171--196}, ISSN = {0234-0852}, } @book {lang:ant, AUTHOR = {Lang, S.}, TITLE = {Algebraic number theory}, EDITION = {Second}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1994}, PAGES = {xiv+357}, ISBN = {0-387-94225-4}, } @book {miyake, author = {Miyake}, title = {Modular forms} } @book {lang:modular, AUTHOR = {Lang, S.}, TITLE = {Introduction to modular forms}, NOTE = {With appendixes by D. Zagier and Walter Feit, Corrected reprint of the 1976 original}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1995}, PAGES = {x+261}, ISBN = {3-540-07833-9}, } @article {lorenzini:abvarred, AUTHOR = {Lorenzini, D.J.}, title = "On the Jacobian of the Modular Curve \protect{$X_0(N)$}", journal = "Preprint" } @article {lorenzini:compgrp, AUTHOR = {Lorenzini, D.J.}, TITLE = {On the group of components of a \protect{N}\'eron model}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik}, VOLUME = {445}, YEAR = {1993}, PAGES = {109--160}, ISSN = {0075-4102}, CODEN = {JRMAA8}, } @article{manin:cyclo, AUTHOR = {Manin, J.I.}, TITLE = {Cyclotomic fields and modular curves}, JOURNAL = {Russian Math. Surveys}, VOLUME = {26}, YEAR = {1971}, NUMBER = {6}, PAGES = {7--78}, } @article{mazur:visthree, author="Mazur, B.", title="Visualizing elements of order three in the Shafarevich-Tate group.", year={1999} } @ARTICLE{mazur:eisenstein, AUTHOR = {Mazur, B.}, TITLE = {Modular curves and the \protect{Eisenstein} ideal}, JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.}, FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques}, NUMBER = {47}, YEAR = {1977}, PAGES = {33--186 (1978)}, ISSN = {0073-8301}, CODEN = {PMIHA6}, } @article{mazur:tower, AUTHOR = {Mazur, B.}, TITLE = {Rational points of abelian varieties with values in towers of number fields}, JOURNAL = {Invent. Math.}, VOLUME = {18}, YEAR = {1972}, PAGES = {183--266}, } @article{mazur:rational, AUTHOR = {Mazur, B.}, TITLE = {Rational isogenies of prime degree (with an appendix by {D}. {G}oldfeld)}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {44}, YEAR = {1978}, NUMBER = {2}, PAGES = {129--162}, ISSN = {0020-9910}, CODEN = {INVMBH}, } @article{mazur:arizona, author="Mazur, B.", title ="Three lectures about the arithmetic of elliptic curves.", journal="To appear in the proceedings from the Arizona Southwest Geometry Winter School", year=1998 } @article{mazur:visord3, author="Mazur, B.", title="Visualizing elements of order three in the Shafarevich-Tate group.", journal="preprint", year=1998 } @article{mestre:graphs, AUTHOR = {Mestre, J.-F.}, TITLE = {La m\'ethode des graphes. \protect{Exemples} et applications}, JOURNAL = {Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata)}, PAGES = {217--242}, PUBLISHER = {Nagoya Univ.}, ADDRESS = {Nagoya}, YEAR = {1986}, } @book {mumford:abvars, AUTHOR = {Mumford, D.}, TITLE = {Abelian varieties}, NOTE = {Tata Institute of Fundamental Research Studies in Mathematics, No. 5 }, PUBLISHER = {Published for the Tata Institute of Fundamental Research, Bombay}, YEAR = {1970}, PAGES = {viii+242}, } @incollection {sturm:cong, AUTHOR = {Sturm, J.}, TITLE = {On the congruence of modular forms}, BOOKTITLE = {Number theory (New York, 1984--1985)}, PAGES = {275--280}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1987}, } @proceedings {MR87m:11004, TITLE = {Number theory}, BOOKTITLE = {Proceedings of the seminar held at the City University of New York, New York, 1984--1985}, EDITOR = {Chudnovsky, D. V. and Chudnovsky, G. V. and Cohn, H. and Nathanson, M. B.}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1987}, PAGES = {vi+324}, ISBN = {3-540-17669-1}, } @book {mumford:geometric, AUTHOR = {Mumford, D. and Fogarty, J. and Kirwan, F.}, TITLE = {Geometric invariant theory}, EDITION = {Third}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1994}, PAGES = {xiv+292}, ISBN = {3-540-56963-4}, } @inproceedings {queen, AUTHOR = {Queen, C.}, TITLE = {The existence of \protect{$p$}-adic \protect{A}belian \protect{${L}$}-functions}, BOOKTITLE = {Number theory and algebra}, PAGES = {263--288}, PUBLISHER = {Academic Press}, ADDRESS = {New York}, YEAR = {1977}, } @book {MR56:11675, TITLE = {Number theory and algebra}, EDITOR = {Zassenhaus, H.}, NOTE = {Collected papers dedicated to Henry B. Mann, Arnold E. Ross, and Olga Taussky-Todd}, PUBLISHER = {Academic Press [Harcourt Brace Jovanovich Publishers]}, ADDRESS = {New York}, YEAR = {1977}, PAGES = {x1vi+393}, ISBN = {0-12-776350-3.}, } @inproceedings {ribet:galoisattached, AUTHOR = {Ribet, K.A.}, TITLE = {Galois representations attached to eigenforms with \protect{N}ebentypus}, BOOKTITLE = {Modular functions of one variable, V (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976)}, PAGES = {17--51. Lecture Notes in Math., Vol. 601}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1977}, } @inproceedings {katz:antwerp350, AUTHOR = {Katz, N.M.}, TITLE = {$p$-adic properties of modular schemes and modular forms}, BOOKTITLE = {Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)}, PAGES = {69--190. Lecture Notes in Mathematics, Vol. 350}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1973}, } @inproceedings {katz:antwerp601, AUTHOR = {Katz, N.M.}, TITLE = {A result on modular forms in characteristic $p$}, BOOKTITLE = {Modular functions of one variable, V (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976)}, PAGES = {53--61. Lecture Notes in Math., Vol. 601}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1977} } @book {slnm601, TITLE = {Modular functions of one variable. {V}}, BOOKTITLE = {Proceedings of the Second International Conference, held at the University of Bonn, Bonn, July 2--14, 1976}, NOTE = {Edited by J.-P. Serre and D. B. Zagier, Lecture Notes in Mathematics, Vol. 601}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1977}, PAGES = {i+294}, } @article{ribet:mestreletter, author = {Ribet, K.A.}, title = {Letter to \protect{M}estre}, year = {November, 1987} }; @article {ribet:modreps, AUTHOR = {Ribet, K.A.}, TITLE = {On modular representations of \protect{${\rm {G}al}(\overline{\bf {Q}}/{\bf {Q}})$} arising from modular forms}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {100}, YEAR = {1990}, NUMBER = {2}, PAGES = {431--476}, ISSN = {0020-9910}, CODEN = {INVMBH}, } @incollection {ribet:report, AUTHOR = {Ribet, K.A.}, TITLE = {Report on mod \protect{$l$} representations of \protect{${\rm {G}al}(\overline{\bf{Q}}/{\bf {Q}})$}}, BOOKTITLE = {Motives (Seattle, WA, 1991)}, PAGES = {639--676}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1994}, } @book {schilling, TITLE = {Arithmetical algebraic geometry. (\protect{P}roceedings of a \protect{C}onference held at \protect{P}urdue \protect{U}niversity, \protect{D}ecember 5--7, 1963)}, EDITOR = {Schilling, O. F. G.}, PUBLISHER = {Harper \& Row Publishers}, ADDRESS = {New York}, YEAR = {1965}, PAGES = {vii+200}, } @article{TOULOUSE, author={Toulouse}, title={\protect{From the \Weil\ conjecture to Fermat's Last Theorem}}, journal={\protect{Annales de la Facult\'e des Sciences de l'Universit\'e de Toulouse}}, volume={11}, year={1990}, pages={116--139}, } @article{serre:congtau, author = {Serre, J.-P.}, title = {Une \protect{interpr\'etation} des congruences relatives \protect{\`a} la fonction \protect{$\tau$} de Ramanujan}, journal = {\protect{S\'eminaire Delange-Pisot-Poitou}}, year = {1967--68}, volume = {\protect{${\roman n}^{\roman o}$ 14}}, note = {English translation: \protect{\tt http://www.rzuser.uni-heidelberg.de/uhb3/Trans.html}} } @book {serre:ladic, AUTHOR = {Serre, J.-P.}, TITLE = {Abelian $l$-adic representations and elliptic curves}, NOTE = {With the collaboration of Willem Kuyk and John Labute, Revised reprint of the 1968 original}, PUBLISHER = {A K Peters Ltd.}, ADDRESS = {Wellesley, MA}, YEAR = {1998}, PAGES = {199}, ISBN = {1-56881-077-6}, } @book {serre:linear, AUTHOR = {Serre, Jean-Pierre}, TITLE = {Linear representations of finite groups}, NOTE = {Translated from the second French edition by Leonard L. Scott, Graduate Texts in Mathematics, Vol. 42}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1977}, PAGES = {x+170}, ISBN = {0-387-90190-6}, } @article{NOMULT, author={Ribet, K.A.}, title = {Lowering the levels of modular representations without multiplicity one}, journal={International Mathematics Research Notices}, year={1991}, pages={15--19} } @incollection {serre:local, AUTHOR = {Serre, J.-P.}, TITLE = {Local class field theory}, BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965)}, PAGES = {128--161}, PUBLISHER = {Thompson, Washington, D.C.}, YEAR = {1967}, } @book {serre:alggroups, AUTHOR = {Serre, J.-P.}, TITLE = {Algebraic groups and class fields}, NOTE = {Translated from the French}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1988}, PAGES = {x+207}, ISBN = {0-387-96648-X}, } @book {serre:arithmetic, AUTHOR = {Serre, J.-P.}, TITLE = {A Course in Arithmetic}, NOTE = {Translated from the French, Graduate Texts in Mathematics, No. 7}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1973}, PAGES = {viii+115}, } @book {serre:localfields, AUTHOR = {Serre, J.-P.}, TITLE = {Local fields}, NOTE = {Translated from the French by Marvin Jay Greenberg}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1979}, PAGES = {viii+241}, ISBN = {0-387-90424-7}, } @article{serre:propgal, author = {Serre, J.-P.}, title = {\protect{Propri\'{e}t\'{e}s} galoisennes de points d'ordre fini des courbes elliptiques}, journal = {Invent. Math.}, volume = {15}, year = {1972}, pages = {259--331} } @article{serre:propres, author={Serre, J.-P.}, title={Valeurs propres des \protect{op\'{e}rateurs} de \protect{Hecke} modulo \protect{$\ell$}}, journal = {\protect{Ast\'{e}risque}}, volume = {24--25}, year = {1975}, pages = {109--117} } @article {serre:conjectures, AUTHOR = {Serre, J.-P.}, TITLE = {Sur les repr\'esentations modulaires de degr\'e \protect{$2$} de \protect{${\rm{G}al}(\overline{\bf {Q}}/{\bf {Q}})$}}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {54}, YEAR = {1987}, NUMBER = {1}, PAGES = {179--230}, ISSN = {0012-7094}, CODEN = {DUMJAO}, } @article {serre-tate, AUTHOR = {Serre, J.-P. and Tate, J.}, TITLE = {Good reduction of abelian varieties}, JOURNAL = {Ann. of Math. (2)}, VOLUME = {88}, YEAR = {1968}, PAGES = {492--517}, } @article{shimura:factors, AUTHOR = {Shimura, G.}, TITLE={On the factors of the jacobian variety of a modular function field}, journal={J. Math. Soc. Japan}, volume={25}, number={3}, year={1973}, pages={523--544}, } @article{shimura:onperiods, author={Shimura, G.}, title={On the periods of modular forms}, journal={Math. Ann.}, volume={229}, pages={211--221}, year={1977} } @article {shimura:surles, AUTHOR = {Shimura, G.}, TITLE = {Sur les int\'egrales attach\'ees aux formes automorphes}, JOURNAL = {J. Math. Soc. Japan}, VOLUME = {11}, YEAR = {1959}, PAGES = {291--311}, } @book {silverman:aec2, AUTHOR = {Silverman, J.H.}, TITLE = {Advanced topics in the arithmetic of elliptic curves}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1994}, PAGES = {xiv+525}, ISBN = {0-387-94328-5}, } @book {silverman:aec, AUTHOR = {Silverman, J.H.}, TITLE = {The arithmetic of elliptic curves}, NOTE = {Corrected reprint of the 1986 original}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1992}, PAGES = {xii+400}, ISBN = {0-387-96203-4}, } @article{stein:compgroup, author = "Stein, W.A.", title = {Component groups of optimal quotients of Jacobians}, journal = {Preprint}, year = {1999} } @article{stein:congruence, author = "Stein, W.A.", title = {Congruences between modular forms}, journal = {Notes}, year = {1999} } @article{generatinghecke, author = "Agashe, A. and Stein, W.A.", title = {Generating the \protect{H}ecke algebra}, journal = {Preprint}, year = {1999} } @article{stein:hecke, author = "Stein, W.A.", title = {\protect{{\tt HECKE}: The} modular forms calculator}, journal = {Software (available online)}, year = {1999} } @article{stein:vissha, author = "Stein, W.A.", title = {Some abelian varieties with visible Shafarevich-Tate groups}, journal = {Preprint}, year = {1999} } @article{stein:periods, author = "Stein, W.A. and Verrill, H.", title = {Computing period lattices associated to newforms}, journal = {Preprint}, year = {1999} } @article{stein:phd, author="Stein, W.", title={Optimal quotients of \protect{$J_0(N)$}}, journal={U.C. Berkeley Ph.D. thesis, in preparation}, year={1999} } @article{tate:nonexistence, author={Tate, J.T.}, title={The non-existence of certain \protect{Galois} extensions of \protect{$\Q$} unramified outside \protect{$2$}}, journal={Contemporary Math.}, volume={174}, year={1994}, pages={153--156} } @incollection {tate:global, AUTHOR = {Tate, J. T.}, TITLE = {Global class field theory}, BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965)}, PAGES = {162--203}, PUBLISHER = {Thompson, Washington, D.C.}, YEAR = {1967}, } @Comment {should be V\'{e}lu but this causes problems.} @inproceedings {velu:groupes, AUTHOR = {Velu, J.}, TITLE = {Groupes de \protect{G}alois attach\'es aux points d'ordre fini des courbes elliptiques sur un corps de nombres, d'apr\`es \protect{J}. \protect{P}. \protect{S}erre}, BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, 1971--1972 (Univ. Bordeaux I, Talence), Exp. No. 30}, PAGES = {12}, PUBLISHER = {Lab. Th\'eorie des Nombres, Centre Nat. Recherche Sci., Talence}, YEAR = {1972}, } @book {MR52:8007, TITLE = {S\'eminaire de {T}h\'eorie des {N}ombres. 1971--1972}, NOTE = {Tenu \`a l'Universit\'e de Bordeaux I, Talence, ann\'ee universitaire 1971--1972}, PUBLISHER = {Laboratoire de Th\'eorie des Nombres, Centre National de Recherche Scientifique, Talence}, YEAR = {1972}, PAGES = {224 pp. (not consecutively paged)}, } @article{diamond:refined, author={Diamond, F.}, title={NOT DONE. The refined conjecture of Serre} } @article{diamond-im, AUTHOR = {Diamond, F. and Im, J.}, TITLE = {Modular forms and modular curves}, BOOKTITLE = {Seminar on Fermat's Last Theorem (Toronto, ON, 1993--1994)}, PAGES = {39--133}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1995}, } @book {MR96f:11004, TITLE = {Seminar on \protect{F}ermat's \protect{L}ast \protect{T}heorem}, EDITOR = {Murty, V. Kumar}, NOTE = {Papers from the seminar held at the Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, 1993--1994}, PUBLISHER = {Published by the American Mathematical Society, Providence, RI}, YEAR = {1995}, PAGES = {x+265}, ISBN = {0-8218-0313-1}, } @proceedings{boston, TITLE = {Modular forms and \protect{F}ermat's last theorem}, EDITOR = {Cornell, G. and Silverman, J.H. and Stevens, G.}, NOTE = {Papers from the Instructional Conference on Number Theory and Arithmetic Geometry held at Boston University, Boston, MA, August 9--18, 1995}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1997}, PAGES = {xx+582}, ISBN = {0-387-94609-8}, } @article{deligne:ladic, author = {Deligne, P.}, title={Formes modulaires et \protect{repr\'{e}sentations $\ell$-adiques.}}, NOTE = {Lecture Notes in Mathematics, Vol. 179}, PUBLISHER = {Springer-Verlag}, booktitle = {\protect{S\'{e}m.} Bourbaki no. 355, 1968/69}, ADDRESS = {Berlin and New York}, year = {1971}, pages = {139--172} } @book {MR48:8389, TITLE = {Modular functions of one variable. {I}{I}}, BOOKTITLE = {Proceedings of the International Summer School, University of Antwerp, RUCA, July 17--August 3, 1972}, EDITOR = {Deligne, Pierre and Kuyk, Willem}, NOTE = {Lecture Notes in Mathematics, Vol. 349}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1973}, PAGES = {iv+598}, } @book {MR48:2080, TITLE = {Modular functions of one variable. {I}{I}{I}}, BOOKTITLE = {Proceedings of the International Summer School, University of Antwerp, RUCA, July 17--August 3, 1972}, EDITOR = {Kuyk, Willem and Serre, J.-P.}, NOTE = {Lecture Notes in Mathematics, Vol. 350}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1973}, PAGES = {iv+350}, } @article{ntl, title = {\protect{NTL: Number} theory library}, author = {Shoup, V.}, } @article{lidia, title = {\protect{LiDIA: C++} number theory library}, author = {Buchmann, J. and others} } @article{cremona-luiz, title = {\protect{C++} matrix classes}, author = {Cremona, J.E. and Luiz F.} } @book {freyetal, TITLE = {On {A}rtin's conjecture for odd 2-dimensional representations}, BOOKTITLE = {On \protect{A}rtin's conjecture for odd $2$-dimensional representations}, EDITOR = {Frey, G.}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1994}, PAGES = {viii+148}, ISBN = {3-540-58387-4}, } @article{winnie, author = {Li, Winnie}, title = {Unfinished reference} } @article {casselman, AUTHOR = {Casselman, W.}, TITLE = {On representations of \protect{${\rm {G}{L}}\sb{2}$} and the arithmetic of modular curves}, BOOKTITLE = {Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)}, PAGES = {107--141. Lecture Notes in Math., Vol. 349}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1973}, } @proceedings {cassels-frohlich, TITLE = {Algebraic number theory}, BOOKTITLE = {Proceedings of the instructional conference held at the University of Sussex, Brighton, September 1--17, 1965}, EDITOR = {Cassels, J. W. S. and Fr{\"o}hlich, A.}, NOTE = {Reprint of the 1967 original}, PUBLISHER = {Academic Press Inc. [Harcourt Brace Jovanovich Publishers]}, ADDRESS = {London}, YEAR = {1986}, PAGES = {xviii+366}, ISBN = {0-12-163251-2}, }