This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2000.7.19) 12 MAR 2002 14:32 **motive_visibility_v6 (motive_visibility_v6.tex LaTeX2e <1999/12/01> patch level 1 Babel and hyphenation patterns for american, french, german, ngerman, i talian, nohyphenation, loaded. (/usr/share/texmf/tex/latex/amscls/amsart.cls Document Class: amsart 2000/10/26 v2.08 \linespacing=\dimen102 \normalparindent=\dimen103 \normaltopskip=\skip41 (/usr/share/texmf/tex/latex/amsmath/amsmath.sty Package: amsmath 2000/07/18 v2.13 AMS math features \@mathmargin=\skip42 For additional information on amsmath, use the `?' option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty Package: amstext 2000/06/29 v2.01 (/usr/share/texmf/tex/latex/amsmath/amsgen.sty File: amsgen.sty 1999/11/30 v2.0 \@emptytoks=\toks14 \ex@=\dimen104 )) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty Package: amsbsy 1999/11/29 v1.2d \pmbraise@=\dimen105 ) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty Package: amsopn 1999/12/14 v2.01 operator names ) \inf@bad=\count79 LaTeX Info: Redefining \frac on input line 211. \uproot@=\count80 \leftroot@=\count81 LaTeX Info: Redefining \overline on input line 307. \classnum@=\count82 \DOTSCASE@=\count83 LaTeX Info: Redefining \ldots on input line 379. LaTeX Info: Redefining \dots on input line 382. LaTeX Info: Redefining \cdots on input line 467. \Mathstrutbox@=\box26 \strutbox@=\box27 \big@size=\dimen106 LaTeX Font Info: Redeclaring font encoding OML on input line 567. LaTeX Font Info: Redeclaring font encoding OMS on input line 568. \macc@depth=\count84 \c@MaxMatrixCols=\count85 \dotsspace@=\muskip10 \c@parentequation=\count86 \dspbrk@lvl=\count87 \tag@help=\toks15 \row@=\count88 \column@=\count89 \maxfields@=\count90 \andhelp@=\toks16 \eqnshift@=\dimen107 \alignsep@=\dimen108 \tagshift@=\dimen109 \tagwidth@=\dimen110 \totwidth@=\dimen111 \lineht@=\dimen112 \@envbody=\toks17 \multlinegap=\skip43 \multlinetaggap=\skip44 \mathdisplay@stack=\toks18 LaTeX Info: Redefining \[ on input line 2666. LaTeX Info: Redefining \] on input line 2667. ) LaTeX Font Info: Try loading font information for U+msa on input line 395. 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LaTeX Font Info: Try loading font information for U+msa on input line 91. (/usr/share/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 91. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 1995/01/05 v2.2e AMS font definitions ) Underfull \hbox (badness 1953) in paragraph at lines 115--115 [][]\OT1/cmr/m/it/8 Key words and phrases.\OT1/cmr/m/n/8 modular form, $\OML/cm m/m/it/8 L$\OT1/cmr/m/n/8 -function, vis-i-bil-ity, Bloch-Kato con-jec-ture, [] LaTeX Font Info: Try loading font information for U+euf on input line 155. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for OT2+wncyr on input line 17 1. (/usr/share/texmf/tex/latex/cyrillic/ot2wncyr.fd File: ot2wncyr.fd 1999/05/31 v3.2 Computer Modern Cyrillic font definitions ) [1] [2] [3] Package amsmath Warning: Foreign command \over; (amsmath) \frac or \genfrac should be used instead (amsmath) on input line 326. [4] Overfull \hbox (5.33505pt too wide) in paragraph at lines 392--394 \OT1/cmr/bx/n/10 Lemma 4.4. $[][]\OT1/cmr/m/n/10 (#^^@[](\OML/cmm/m/it/10 j\OT1 /cmr/m/n/10 )) = 0$ \OT1/cmr/m/it/10 if $\OML/cmm/m/it/10 A\OT1/cmr/m/n/10 [\OM L/cmm/m/it/10 ^^U\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 is an ir-re-ducible rep-re -sen-ta-tion of $[]\OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 =\U/msb/m/n/10 Q\OT1/cmr /m/n/10 )$\OT1/cmr/m/it/10 . [] [5] [6] Overfull \hbox (12.70718pt too wide) in paragraph at lines 541--550 \OT1/cmr/m/n/10 ducibil-ity, $\OML/cmm/m/it/10 H[]\OT1/cmr/m/n/10 (\U/msb/m/n/1 0 Q\OML/cmm/m/it/10 ; A\OT1/cmr/m/n/10 [\U/euf/m/n/10 q\OT1/cmr/m/n/10 ](\OML/c mm/m/it/10 k=\OT1/cmr/m/n/10 2))$ is triv-ial, so $\OML/cmm/m/it/10 H[]\OT1/cmr /m/n/10 (\U/msb/m/n/10 Q\OML/cmm/m/it/10 ; A\OT1/cmr/m/n/10 [\U/euf/m/n/10 q\OT 1/cmr/m/n/10 ](\OML/cmm/m/it/10 k=\OT1/cmr/m/n/10 2))$ in-jects into $\OML/cmm/ m/it/10 H[]\OT1/cmr/m/n/10 (\U/msb/m/n/10 Q\OML/cmm/m/it/10 ; A[]\OT1/cmr/m/n/1 0 (\OML/cmm/m/it/10 k=\OT1/cmr/m/n/10 2))$, [] [7] [8] Overfull \hbox (1.97449pt too wide) in paragraph at lines 688--702 \OT1/cmr/m/n/10 The Ga-lois or-bits are or-dered first by the de-gree of $\U/ms b/m/n/10 Q\OT1/cmr/m/n/10 ([] \OML/cmm/m/it/10 ; a[]; []\OT1/cmr/m/n/10 )$, the n by $\OMS/cmsy/m/n/10 j[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 a[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 ))\OMS/cmsy/m/n/10 j$ [] [9] [10] [11] Overfull \hbox (4.50038pt too wide) in paragraph at lines 883--883 []\OT1/cmr/m/sc/8 University of Sheffield, De-part-ment of Pure Math-e-mat-ics, Hicks Build-ing, Hounsfield [] [12] (motive_visibility_v6.aux) ) Here is how much of TeX's memory you used: 1729 strings out of 20898 18156 string characters out of 196686 68416 words of memory out of 350001 4512 multiletter control sequences out of 10000+15000 13310 words of font info for 51 fonts, out of 400000 for 1000 175 hyphenation exceptions out of 1000 34i,17n,32p,305b,412s stack positions out of 1500i,100n,500p,50000b,4000s Output written on motive_visibility_v6.dvi (12 pages, 63112 bytes).