This is TeX, Version 3.14159 (C version 6.1) (format=latex 98.5.7) 24 SEP 1998 06:54 **ribetnotes.tex (ribetnotes.tex LaTeX2e <1996/12/01> patch level 1 Babel and hyphenation patterns for american, german, loaded. (/usr/lib/texmf/texmf/tex/latex/base/book.cls Document Class: book 1996/10/31 v1.3u Standard LaTeX document class (/usr/lib/texmf/texmf/tex/latex/base/bk12.clo File: bk12.clo 1996/10/31 v1.3u Standard LaTeX file (size option) ) \c@part=\count79 \c@chapter=\count80 \c@section=\count81 \c@subsection=\count82 \c@subsubsection=\count83 \c@paragraph=\count84 \c@subparagraph=\count85 \c@figure=\count86 \c@table=\count87 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) (/usr/lib/texmf/texmf/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 1996/11/03 v2.2c \@emptytoks=\toks14 \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 129. ) (/usr/lib/texmf/texmf/tex/latex/amslatex/amsmath.sty Package: amsmath 1996/11/01 v1.2c AMS math features \@mathmargin=\skip43 (/usr/lib/texmf/texmf/tex/latex/amslatex/amstext.sty Package: amstext 1996/10/28 v1.2b (/usr/lib/texmf/texmf/tex/latex/amslatex/amsgen.sty File: amsgen 1996/10/29 v1.2b \@emptytoks=\toks15 \ex@=\dimen103 )) (/usr/lib/texmf/texmf/tex/latex/amslatex/amsbsy.sty Package: amsbsy 1996/10/28 v1.2b \pmbraise@=\dimen104 ) (/usr/lib/texmf/texmf/tex/latex/amslatex/amsopn.sty Package: amsopn 1996/10/28 v1.2b operator names ) LaTeX Info: Redefining \frac on input line 188. \uproot@=\count88 \leftroot@=\count89 \classnum@=\count90 \DOTSCASE@=\count91 LaTeX Info: Redefining \dots on input line 335. LaTeX Info: Redefining \ldots on input line 418. LaTeX Info: Redefining \cdots on input line 422. \Mathstrutbox@=\box26 \strutbox@=\box27 \big@size=\dimen105 LaTeX Font Info: Redeclaring font encoding OML on input line 500. LaTeX Font Info: Redeclaring font encoding OMS on input line 501. \skewcharcount@=\count92 \familycount@=\count93 \pointcount@=\count94 \accentdimen@=\dimen106 \accentmu@=\count95 \minaw@=\dimen107 \c@MaxMatrixCols=\count96 \dotsspace@=\muskip10 \c@parentequation=\count97 \dspbrk@lvl=\count98 \tag@help=\toks16 \row@=\count99 \column@=\count100 \maxfields@=\count101 \andhelp@=\toks17 \eqnshift@=\dimen108 \alignsep@=\dimen109 \tagshift@=\dimen110 \tagwidth@=\dimen111 \totwidth@=\dimen112 \lineht@=\dimen113 \@envbody=\toks18 \multlinegap=\skip44 \multlinetaggap=\skip45 ) (/usr/lib/texmf/texmf/tex/latex/amslatex/amsthm.sty Package: amsthm 1996/10/24 v1.2d \thm@style=\toks19 \thm@bodyfont=\toks20 \thm@headfont=\toks21 \thm@notefont=\toks22 \thm@headpunct=\toks23 \thm@preskip=\skip46 \thm@postskip=\skip47 ) (/usr/lib/texmf/texmf/tex/latex/amslatex/amscd.sty Package: amscd 1996/10/28 v1.2b \athelp@=\toks24 \bigaw@=\dimen114 \minCDarrowwidth=\dimen115 ) (/usr/lib/texmf/texmf/tex/latex/base/makeidx.sty Package: makeidx 1995/04/19 v1.0j Standard LaTeX package ) \@indexfile=\write3 Writing index file ribetnotes.idx LaTeX Info: Redefining \sl2 on input line 189. LaTeX Info: Redefining \sl2z on input line 190. \c@thm=\count102 (ribetnotes.aux) LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 240. LaTeX Font Info: ... okay on input line 240. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 240. LaTeX Font Info: ... okay on input line 240. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 240. LaTeX Font Info: ... okay on input line 240. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 240. LaTeX Font Info: ... okay on input line 240. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 240. LaTeX Font Info: ... okay on input line 240. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 240. LaTeX Font Info: ... okay on input line 240. LaTeX Font Info: Try loading font information for U+msa on input line 242. (/usr/lib/texmf/texmf/tex/latex/amsfonts/umsa.fd File: Umsa.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 242. (/usr/lib/texmf/texmf/tex/latex/amsfonts/umsb.fd File: Umsb.fd 1995/01/05 v2.2e AMS font definitions ) [1 ] [2 ] [3] [4 ] (ribetnotes.toc [5] [6] [7]) \tf@toc=\write4 [8] Chapter 1. LaTeX Font Info: Try loading font information for OMS+cmr on input line 291. (/usr/lib/texmf/texmf/tex/latex/base/omscmr.fd File: omscmr.fd 1997/01/14 v2.5a Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <12> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 291. Overfull \hbox (6.69891pt too wide) in paragraph at lines 340--340 []\OT1/cmr/bx/n/14.4 Galois Rep-re-sen-ta-tions (Taniyama, Shimura, Mumford-Tat e) [] [1 ] Overfull \hbox (1.89725pt too wide) detected at line 347 $[] \OMS/cmsy/m/n/12 !$ [] Overfull \hbox (1.89725pt too wide) detected at line 347 $[] \OMS/cmsy/m/n/12 !$ [] [2] [3] [4 ] Chapter 2. [5] Overfull \hbox (2.22252pt too wide) detected at line 521 $[] \OMS/cmsy/m/n/12 !$ [] Overfull \hbox (2.22252pt too wide) detected at line 521 $[] \OMS/cmsy/m/n/12 !$ [] [6] [7] [8] Chapter 3. [9 ] Overfull \hbox (2.22252pt too wide) detected at line 745 $[] \OMS/cmsy/m/n/12 !$ [] [10] [11] [12] [13] [14 ] Chapter 4. [15] [16] [17] [18 ] Chapter 5. [19] [20] [21] [22 ] Chapter 6. [23] [24] [25] [26] [27] [28 ] Chapter 7. [29] [30] [31] [32 ] Chapter 8. [33] [34] [35] [36] Chapter 9. Overfull \hbox (17.60516pt too wide) in paragraph at lines 1927--1932 []\OT1/cmr/m/n/12 Suppose $^^@ = ^^@[](\OML/cmm/m/it/12 N\OT1/cmr/m/n/12 )$, th en the de-gree of the cov-er-ing is the in-dex $([] \OML/cmm/m/it/12 =\OMS/cmsy /m/n/12 f^^F\OT1/cmr/m/n/12 1\OMS/cmsy/m/n/12 g \OT1/cmr/m/n/12 : [] [37 ] Overfull \hbox (2.22252pt too wide) detected at line 1981 $[] \OMS/cmsy/m/n/12 !$ [] [38] [39] [40] Chapter 10. [41 ] Overfull \hbox (3.16644pt too wide) in paragraph at lines 2168--2172 []\OT1/cmr/m/it/12 Let $\OML/cmm/m/it/12 E[]$ \OT1/cmr/m/it/12 and $\OML/cmm/m/ it/12 E[]$ \OT1/cmr/m/it/12 be el-lip-tic curves de-fined over $\OML/cmm/m/it/1 2 K$ \OT1/cmr/m/it/12 with equal $\OML/cmm/m/it/12 j$\OT1/cmr/m/it/12 -invarian ts, [] [42] [43] Overfull \hbox (2.00002pt too wide) detected at line 2381 $[] \OMS/cmsy/m/n/12 !$ [] [44] [45] [46] Chapter 11. [47 ] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58 ] Chapter 12. [59] [60] [61] Overfull \hbox (17.60292pt too wide) in paragraph at lines 3274--3276 []\OT1/cmr/m/it/12 Let the no-ta-tion be as above. Then $[]\OT1/cmr/m/n/12 (\OM L/cmm/m/it/12 ^^Z[]\OT1/cmr/m/n/12 ([][])) = \OML/cmm/m/it/12 a[]$ \OT1/cmr/m/i t/12 and $[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 ^^Z[]\OT1/cmr/m/n/12 ([][])) = [] [62] [63] [64] [65] [66 ] Chapter 13. [67] Overfull \hbox (29.8586pt too wide) in paragraph at lines 3553--3560 []\OT1/cmr/m/n/12 The Hecke op-er-a-tors $\OML/cmm/m/it/12 T[]$ \OT1/cmr/m/n/12 act on the space $\OML/cmm/m/it/12 S[]\OT1/cmr/m/n/12 (^^@[](\OML/cmm/m/it/12 N\OT1/cmr/m/n/12 ))$. Let $\OT1/cmr/bx/n/12 T \OT1/cmr/m/n/12 = \OT1/cmr/bx/n/1 2 Z\OT1/cmr/m/n/12 [[] \OML/cmm/m/it/12 ; T[]; [] \OT1/cmr/m/n/12 ] \OMS/cmsy/ m/n/12 ^^Z []\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 S[]\OT1/cmr/m/n/12 (^^@[](\OML/c mm/m/it/12 N\OT1/cmr/m/n/12 )))$ [] Overfull \hbox (0.10248pt too wide) in paragraph at lines 3553--3560 \OT1/cmr/m/n/12 and re-call that $\OT1/cmr/bx/n/12 T$ \OT1/cmr/m/n/12 is a com- mu-ta-tive ring which is a $\OT1/cmr/bx/n/12 Z$\OT1/cmr/m/n/12 -module of rank equal to $[][] \OML/cmm/m/it/12 S[]\OT1/cmr/m/n/12 (^^@[](\OML/cmm/m/it/12 N\OT 1/cmr/m/n/12 ))$. [] [68] [69] [70] [71] Overfull \hbox (13.56808pt too wide) in paragraph at lines 3889--3895 []\OT1/cmr/m/n/12 The \OT1/cmr/bx/n/12 Pon-tr-ja-gin dual \OT1/cmr/m/n/12 of a mod-ule $\OML/cmm/m/it/12 M$ \OT1/cmr/m/n/12 is the mod-ule $\OML/cmm/m/it/12 M [] \OT1/cmr/m/n/12 := [](\OML/cmm/m/it/12 M; \OT1/cmr/bx/n/12 Q\OML/cmm/m/it/12 =\OT1/cmr/bx/n/12 Z\OT1/cmr/m/n/12 )$ [] [72] [73] Overfull \hbox (1.36858pt too wide) in paragraph at lines 4004--4009 \OT1/cmr/m/n/12 But $[][] \OMS/cmsy/m/n/12 []\OT1/cmr/bx/n/12 C \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 L \OMS/cmsy/m/n/12 [] \OT1/cmr/bx/n/12 C$ \OT1/cmr/m/n/12 is free of rank $2$ over $\OT1/cmr/bx/n/ 12 T \OMS/cmsy/m/n/12 \OT1/cmr/bx/n/12 C$\OT1/cmr/m/n/12 . There-fore the prod-uct $[][] [][] \OMS/c msy/m/n/12 []\OT1/cmr/bx/n/12 C$ [] [74] [75] [76] [77] [78] [79] [80 ] Chapter 14. Overfull \hbox (2.07521pt too wide) in paragraph at lines 4374--4377 \OT1/cmr/m/n/12 For each $\OML/cmm/m/it/12 w\OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 p$ \OT1/cmr/m/n/12 let the in-er-tia group $\OML/cmm/m/it/12 I[]$ \OT1/cmr/m/n/ 12 be the ker-nel of the map from $\OML/cmm/m/it/12 D[]$ \OT1/cmr/m/n/12 into $ [](\OMS/cmsy/m/n/12 O[]\OML/cmm/m/it/12 =w; \OT1/cmr/bx/n/12 Z\OML/cmm/m/it/12 =p\OT1/cmr/bx/n/12 Z\OT1/cmr/m/n/12 )$. [] [81] [82] [83] Overfull \hbox (30.82103pt too wide) in paragraph at lines 4524--4524 []\OT1/cmr/bx/n/17.28 Adelic Rep-re-sen-ta-tions As-so-ci-ated to Mod-u-lar For ms [] [84] [85] [86] [87] [88] [89] [90 ] Chapter 15. [91] [92] [93] [94] [95] [96] [97] [98] Overfull \hbox (19.31454pt too wide) has occurred while \output is active \OT1/cmr/m/sl/12 15.6. THE WEIGHT IN SERRE'S CONJECTURES ON MODULAR REPRESENTA TIONS \OT1/cmr/m/n/12 99 [] [99] [100] [101] [102] [103] Overfull \hbox (0.79074pt too wide) detected at line 5717 $[] \OMS/cmsy/m/n/12 !$ [] [104] Chapter 16. [105 ] [106] [107] [108] Chapter 17. [109 ] [110] [111] [112] [113] [114 ] Chapter 18. [115] [116] Overfull \hbox (5.39168pt too wide) in paragraph at lines 6385--6394 \OML/cmm/m/it/12 "$\OT1/cmr/m/n/12 , ($\OML/cmm/m/it/12 "$ \OT1/cmr/m/n/12 Diri ch-let char-ac-ter ram-i-fied at primes in $\OML/cmm/m/it/12 N[]$\OT1/cmr/m/n/1 2 ). Get a form of level $[]([][] \OML/cmm/m/it/12 p[]; N\OT1/cmr/m/n/12 (\OML/ cmm/m/it/12 f\OT1/cmr/m/n/12 ))\OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 N[]$\OT1/cmr/ m/n/12 . [] [117] [118] [119] [120] [121] [122] [123] [124] [125] Overfull \hbox (2.22252pt too wide) detected at line 6948 $[] \OMS/cmsy/m/n/12 !$ [] [126] Overfull \hbox (2.22252pt too wide) detected at line 6995 $[] \OMS/cmsy/m/n/12 !$ [] Overfull \hbox (0.7111pt too wide) detected at line 7006 $[] \OMS/cmsy/m/n/12 !$ [] [127] Overfull \hbox (0.7111pt too wide) detected at line 7071 $[] \OMS/cmsy/m/n/12 !$ [] LaTeX Font Info: Font shape `OMS/cmr/m/it' in size <12> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 7081. [128] [129] [130] [131] [132 ] [133 ] (ribetnotes.ind [134] [135] [136 ]) (ribetnotes.aux) ) Here is how much of TeX's memory you used: 1309 strings out of 10906 12125 string characters out of 72188 64025 words of memory out of 262141 4155 multiletter control sequences out of 9500 21229 words of font info for 81 fonts, out of 150000 for 255 14 hyphenation exceptions out of 607 28i,15n,22p,235b,315s stack positions out of 300i,40n,60p,3000b,4000s Output written on ribetnotes.dvi (144 pages, 537028 bytes).