This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2000.7.19) 12 OCT 2000 15:18 **index.tex (index.tex LaTeX2e <1999/12/01> patch level 1 Babel and hyphenation patterns for american, french, german, ngerman, i talian, nohyphenation, loaded. 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(macros.tex (/usr/share/texmf/tex/latex/amsmath/amsmath.sty Package: amsmath 2000/01/15 v2.05 AMS math features \@mathmargin=\skip43 For additional information on amsmath, use the `?' option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty Package: amstext 1999/11/15 v2.0 (/usr/share/texmf/tex/latex/amsmath/amsgen.sty File: amsgen.sty 1999/11/30 v2.0 \@emptytoks=\toks21 \ex@=\dimen137 )) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty Package: amsbsy 1999/11/29 v1.2d \pmbraise@=\dimen138 ) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty Package: amsopn 1999/12/14 v2.01 operator names ) \inf@bad=\count97 LaTeX Info: Redefining \frac on input line 198. \uproot@=\count98 \leftroot@=\count99 LaTeX Info: Redefining \overline on input line 302. \classnum@=\count100 \DOTSCASE@=\count101 LaTeX Info: Redefining \ldots on input line 376. LaTeX Info: Redefining \dots on input line 379. 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LaTeX Info: Redefining \] on input line 2595. ) (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 1997/09/17 v2.2e \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 133. ) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty Package: amssymb 1996/11/03 v2.2b ) (/usr/share/texmf/tex/latex/amscls/amsthm.sty Package: amsthm 2000/01/17 v2.03 \thm@style=\toks25 \thm@bodyfont=\toks26 \thm@headfont=\toks27 \thm@notefont=\toks28 \thm@headpunct=\toks29 \thm@preskip=\skip46 \thm@postskip=\skip47 \thm@headsep=\skip48 \dth@everypar=\toks30 ) \c@theorem=\count108 \c@listnum=\count109 ) (index.aux) \openout1 = `index.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 33. LaTeX Font Info: ... okay on input line 33. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 33. LaTeX Font Info: ... okay on input line 33. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 33. LaTeX Font Info: ... okay on input line 33. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 33. LaTeX Font Info: ... okay on input line 33. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 33. LaTeX Font Info: ... okay on input line 33. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 33. LaTeX Font Info: ... okay on input line 33. LaTeX Font Info: Try loading font information for U+msa on input line 34. (/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 34. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 1995/01/05 v2.2e AMS font definitions ) [1 ] LaTeX Font Info: Try loading font information for OMS+cmr on input line 127. (/usr/share/texmf/tex/latex/base/omscmr.fd File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 127. [2] [3] LaTeX Font Info: Try loading font information for U+euf on input line 231. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 1995/01/05 v2.2e AMS font definitions ) Overfull \hbox (2.07338pt too wide) in paragraph at lines 265--269 \OT1/cmr/m/n/10 In [[]], Ru-bin gives an ac-count of Koly-va-gin's proof of fin ite-ness of $[](\OML/cmm/m/it/10 E=\OT1/cmr/bx/n/10 Q\OT1/cmr/m/n/10 )[\OML/cmm /m/it/10 p[]\OT1/cmr/m/n/10 ]$, [] [4] [5] [6] [7] Overfull \hbox (0.63487pt too wide) in paragraph at lines 519--527 \OML/cmm/m/it/10 ^^N\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )$ is an -ni-hi-lated by $\OML/cmm/m/it/10 b\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 p; n\OT1/c mr/m/n/10 )$, which con-tra-dic-tion our ini-tial as-sump-tion about $\OML/cmm/ m/it/10 x$\OT1/cmr/m/n/10 . [] [8] [9] [10] [11] [12] (index.bbl Underfull \hbox (badness 1852) in paragraph at lines 56--59 []\OT1/cmr/m/n/10 W.G. Mc-Cal-lum, \OT1/cmr/m/it/10 Koly-va-gin's work on Shafa revich-Tate groups\OT1/cmr/m/n/10 , $\OML/cmm/m/it/10 L$\OT1/cmr/m/n/10 - [] [13]) [14] (index.aux) ) Here is how much of TeX's memory you used: 3815 strings out of 20898 40891 string characters out of 196686 128125 words of memory out of 350001 6711 multiletter control sequences out of 10000+15000 21126 words of font info for 83 fonts, out of 400000 for 1000 14 hyphenation exceptions out of 1000 31i,21n,24p,239b,486s stack positions out of 1500i,100n,500p,50000b,4000s Output written on index.dvi (14 pages, 62024 bytes).