This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) (format=pdflatex 2008.12.28) 23 JUL 2009 00:53 entering extended mode %&-line parsing enabled. **kolyvagin-structure_of_selmer_groups.tex (./kolyvagin-structure_of_selmer_groups.tex LaTeX2e <2005/12/01> Babel and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, german-x-2008-06-18, ngerman-x-2008-06-18, ancientgreek, ibycus, ar abic, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danish, dutc h, esperanto, estonian, farsi, finnish, french, galician, german, ngerman, mono greek, greek, hungarian, icelandic, indonesian, interlingua, irish, italian, la tin, lithuanian, mongolian, mongolian2a, bokmal, nynorsk, polish, portuguese, r omanian, russian, sanskrit, serbian, slovak, slovenian, spanish, swedish, turki sh, ukenglish, ukrainian, uppersorbian, welsh, loaded. (/usr/local/texlive/2008/texmf-dist/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/local/texlive/2008/texmf-dist/tex/latex/base/size12.clo File: size12.clo 2005/09/16 v1.4f Standard LaTeX file (size option) ) \c@part=\count79 \c@section=\count80 \c@subsection=\count81 \c@subsubsection=\count82 \c@paragraph=\count83 \c@subparagraph=\count84 \c@figure=\count85 \c@table=\count86 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) \@input{macros.aux} \openout2 = `macros.aux'. (./macros.tex (/usr/local/texlive/2008/texmf-dist/tex/latex/amsmath/amsmath.sty Package: amsmath 2000/07/18 v2.13 AMS math features \@mathmargin=\skip43 For additional information on amsmath, use the `?' option. 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LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 15. LaTeX Font Info: ... okay on input line 15. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 15. LaTeX Font Info: ... okay on input line 15. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 15. LaTeX Font Info: ... okay on input line 15. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 15. LaTeX Font Info: ... okay on input line 15. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 15. LaTeX Font Info: ... okay on input line 15. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 15. LaTeX Font Info: ... okay on input line 15. LaTeX Font Info: Checking defaults for OT2/cmr/m/n on input line 15. LaTeX Font Info: Try loading font information for OT2+cmr on input line 15. (/usr/local/texlive/2008/texmf-dist/tex/latex/cyrillic/ot2cmr.fd File: ot2cmr.fd 2001/08/11 v3.2c Computer Modern Cyrillic font definitions ) LaTeX Font Info: ... okay on input line 15. LaTeX Font Info: Try loading font information for U+msa on input line 16. (/usr/local/texlive/2008/texmf-dist/tex/latex/amsfonts/umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 16. (/usr/local/texlive/2008/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) Overfull \hbox (4.66534pt too wide) in paragraph at lines 18--22 []\OT1/cmr/m/n/12 The pa-per con-tains some ap-pli-ca-tions of ex-plicit co-ho- mol-ogy classes (which [] Overfull \hbox (24.1318pt too wide) in paragraph at lines 36--36 []\OT1/cmr/bx/n/17.28 Selmer groups and ex-plicit co-ho-mol-ogy classes [] [1 {/usr/local/texlive/2008/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] Overfull \hbox (13.1929pt too wide) in paragraph at lines 45--49 \OT1/cmr/m/n/12 If $\OML/cmm/m/it/12 L=R$ \OT1/cmr/m/n/12 is a Ga-lois ex-ten-s ion, then $\OML/cmm/m/it/12 G\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 L=R\OT1/cmr/m/n/ 12 )$ de-notes its Ga-lois group, $\OML/cmm/m/it/12 H[]\OT1/cmr/m/n/12 (\OML/cm m/m/it/12 R; A\OT1/cmr/m/n/12 ) := [] LaTeX Font Info: Try loading font information for OT2+wncyr on input line 55 . (/usr/local/texlive/2008/texmf-dist/tex/latex/cyrillic/ot2wncyr.fd File: ot2wncyr.fd 1999/12/17 v3.2a Computer Modern Cyrillic font definitions ) [2] [3] Overfull \hbox (2.37303pt too wide) in paragraph at lines 170--176 []\OT1/cmr/m/n/12 Let $\OML/cmm/m/it/12 m[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 ^^ U\OT1/cmr/m/n/12 )$ be the max-i-mal non-neg-a-tive in-te-ger such that $\OML/c mm/m/it/12 P[] \OMS/cmsy/m/n/12 2 \OML/cmm/m/it/12 `[]E\OT1/cmr/m/n/12 (\OML/cm m/m/it/12 K[]\OT1/cmr/m/n/12 )$. [] [4] [5] [6] [7] Overfull \hbox (7.99338pt too wide) in paragraph at lines 407--410 \OT1/cmr/bx/n/12 Conjecture 2.7. \OT1/cmr/m/it/12 There ex-ist $\OML/cmm/m/it/1 2 ^^W \OMS/cmsy/m/n/12 2 f\OT1/cmr/m/n/12 0\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 1 \OMS/cmsy/m/n/12 g$ \OT1/cmr/m/it/12 and a sub-group $\OML/cmm/m/it/12 V \OMS/c msy/m/n/12 ^^Z \OT1/cmr/m/n/12 (\OML/cmm/m/it/12 E\OT1/cmr/m/n/12 (\OML/cmm/m/i t/12 K\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 =E\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 K\O T1/cmr/m/n/12 )[])[]$ [] [8] [9] Underfull \hbox (badness 1454) in paragraph at lines 466--468 []\OT1/cmr/m/n/12 Kolyvagin, V.A.: Eu-ler sys-tems, Birkh^^?auser vol-ume in ho nor of [] [10] (./kolyvagin-structure_of_selmer_groups.aux) LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right. ) Here is how much of TeX's memory you used: 1735 strings out of 493876 17879 string characters out of 1150567 72622 words of memory out of 3000000 5021 multiletter control sequences out of 10000+50000 15711 words of font info for 60 fonts, out of 3000000 for 5000 714 hyphenation exceptions out of 8191 31i,15n,24p,270b,226s stack positions out of 5000i,500n,10000p,200000b,50000s Output written on kolyvagin-structure_of_selmer_groups.pdf (10 pages, 168457 by tes). PDF statistics: 119 PDF objects out of 1000 (max. 8388607) 0 named destinations out of 1000 (max. 131072) 1 words of extra memory for PDF output out of 10000 (max. 10000000)