% Session SMF l'Etat de la Recherche, Grenoble, 25-26-27 Novembre 1994
% Texte pour Panoramas et Synth\`eses
% J. Bertin, J.P. Demailly, Ch. Peters, L. Illusie
% Plain-TeX macro file pour Panoramas et Synth\`eses
% (Version adapt\'ee par J.P. Demailly)

% page setting
% \magnification=1000 \voffset=24mm \hoffset=14mm
% \magnification=1200 \voffset=7mm \hoffset=1mm
\hfuzz=3pt
\pretolerance=500 \tolerance=1000 \brokenpenalty=5000
\hsize=13cm
\vsize=19cm
\parskip2pt plus 1.5pt minus 0.5pt
\parindent=12pt
\abovedisplayskip=12pt plus 3pt minus 4pt
\belowdisplayskip=11pt plus 3pt minus 4pt
\abovedisplayshortskip=6pt plus 3pt
\belowdisplayshortskip=12pt plus 3pt minus 4pt
\smallskipamount=3pt plus 1pt minus 1pt
\medskipamount=6pt plus 2pt minus 2pt
\bigskipamount=12pt plus 4pt minus 4pt
\normalbaselineskip=12pt
\setbox\strutbox=\hbox{\vrule height8.5pt depth3.5pt width0pt}%

%------------------------------------------------------------------------------
%              french dactylography  
%------------------------------------------------------------------------------
\def\sl{\it}

\catcode`\@=11

\catcode`\;=\active
\def;{\relax\ifhmode\ifdim\lastskip>\z@\unskip\fi
\kern\fontdimen2 \font\kern -1.2 \fontdimen3 \font\fi\string;}
 
\catcode`\:=\active
\def:{\relax\ifhmode\ifdim\lastskip>\z@\unskip\fi\penalty\@M\ \fi\string:}
 
\catcode`\!=\active
\def!{\relax\ifhmode\ifdim\lastskip>\z@
\unskip\fi\kern\fontdimen2 \font \kern -1.1 \fontdimen3 \font\fi\string!}
 
\catcode`\?=\active
\def?{\relax\ifhmode\ifdim\lastskip>\z@
\unskip\fi\kern\fontdimen2 \font \kern -1.1 \fontdimen3 \font\fi\string?}
 
\def\^#1{\if#1i{\accent"5E\i}\else{\accent"5E #1}\fi}
\def\"#1{\if#1i{\accent"7F\i}\else{\accent"7F #1}\fi}
 
\frenchspacing
%-------------------------------------------------------------------------------
% new fonts definitions
%-------------------------------------------------------------------------------
\font\seventeenbf=cmbx10 at 17.28pt
\font\seventeenbfit=cmmib10 at 17.28pt
\font\seventeenbsy=cmbsy10 at 17.28pt
\font\fourteenbf=cmbx10 at 14.4pt
\font\fourteenbfit=cmmib10 at 14.4pt
\font\fourteenbsy=cmbsy10 at 14.4pt
\font\twelvei=cmmi10 at 12pt
\font\twelvebf=cmbx10 at 12pt
\font\twelvebfit=cmmib10 at 12pt
\font\twelverm=cmr10 at 12pt
\font\twelvesy=cmsy10 at 12pt
\font\twelvebsy=cmbsy10 at 12pt 
\font\tenbsy=cmbsy10
\font\eightbsy=cmbsy8
\font\sevenbsy=cmbsy7
\font\sixbsy=cmbsy6
\font\fivebsy=cmbsy5
\newfam\bsyfam
  \textfont\bsyfam=\tenbsy
  \scriptfont\bsyfam=\sevenbsy
  \scriptscriptfont\bsyfam=\fivebsy
\def\bsy{\fam\bsyfam\tenbsy} 
\font\tenmsa=msam10
\font\sevenmsa=msam7
\font\fivemsa=msam5
\newfam\msafam
  \textfont\msafam=\tenmsa
  \scriptfont\msafam=\sevenmsa
  \scriptscriptfont\msafam=\fivemsa
\def\msa{\fam\msafam\tenmsa} 
\font\tenmsb=msbm10
\font\sevenmsb=msbm7
\font\fivemsb=msbm5
\newfam\msbfam
  \textfont\msbfam=\tenmsb
  \scriptfont\msbfam=\sevenmsb
  \scriptscriptfont\msbfam=\fivemsb
\def\Bbb{\fam\msbfam\tenmsb}
\font\twelveCalbf=eusb10 at 12pt
\font\tenCal=eusm10
\font\eightCal=eusm8
\font\sevenCal=eusm7
\font\fiveCal=eusm5
\newfam\Calfam
  \textfont\Calfam=\tenCal
  \scriptfont\Calfam=\sevenCal
  \scriptscriptfont\Calfam=\fiveCal
\def\Cal{\fam\Calfam\tenCal}
\font\teneuf=eufm10
\font\seveneuf=eufm7
\font\fiveeuf=eufm5
\newfam\euffam
  \textfont\euffam=\teneuf
  \scriptfont\euffam=\seveneuf
  \scriptscriptfont\euffam=\fiveeuf
\def\euf{\fam\euffam\teneuf}

\font\tenbfit=cmmib10
\font\eightbfit=cmmib8
\font\sevenbfit=cmmib7
\font\sixbfit=cmmib6
\font\fivebfit=cmmib5
\newfam\bfitfam
  \textfont\bfitfam=\tenbfit
  \scriptfont\bfitfam=\sevenbfit
  \scriptscriptfont\bfitfam=\fivebfit
\def\bfit{\fam\bfitfam\tenbfit}

\font\eightrm=cmr8
\font\eighti=cmmi8
\font\eightsy=cmsy8
\font\eightbf=cmbx8
\font\eighttt=cmtt8
\font\eightit=cmti8
\font\eightsl=cmsl8
\font\eightmsa=msam8
\font\eightmsb=msbm8
\font\sixrm=cmr6
\font\sixi=cmmi6
\font\sixsy=cmsy6
\font\sixbf=cmbx6
%---------------------------------------------------------------------
% changing font sizes
%---------------------------------------------------------------------
\catcode`\@=11
\def\eightpoint{%
  \textfont0=\eightrm \scriptfont0=\sixrm \scriptscriptfont0=\fiverm
  \def\rm{\fam\z@\eightrm}%
  \textfont1=\eighti \scriptfont1=\sixi \scriptscriptfont1=\fivei
  \def\oldstyle{\fam\@ne\eighti}%
  \textfont2=\eightsy \scriptfont2=\sixsy \scriptscriptfont2=\fivesy
  \textfont\itfam=\eightit
  \def\it{\fam\itfam\eightit}%
  \textfont\slfam=\eightsl
  \def\sl{\fam\slfam\eightsl}%
  \textfont\bffam=\eightbf \scriptfont\bffam=\sixbf
  \scriptscriptfont\bffam=\fivebf
  \def\bf{\fam\bffam\eightbf}%
  \textfont\ttfam=\eighttt
  \def\tt{\fam\ttfam\eighttt}%
  \textfont\msbfam=\eightmsb
  \def\Bbb{\fam\msbfam\eightmsb}%
  \abovedisplayskip=9pt plus 2pt minus 6pt
  \abovedisplayshortskip=0pt plus 2pt
  \belowdisplayskip=9pt plus 2pt minus 6pt
  \belowdisplayshortskip=5pt plus 2pt minus 3pt
  \smallskipamount=2pt plus 1pt minus 1pt
  \medskipamount=4pt plus 2pt minus 1pt
  \bigskipamount=9pt plus 3pt minus 3pt
  \normalbaselineskip=9pt
  \setbox\strutbox=\hbox{\vrule height7pt depth2pt width0pt}%
  \let\bigf@ntpc=\eightrm \let\smallf@ntpc=\sixrm
  \normalbaselines\rm}

\def\seventeenpointbf{%
 \textfont0=\seventeenbf  \scriptfont0=\twelvebf  \scriptscriptfont0=\eightbf
 \textfont1=\seventeenbfit\scriptfont1=\twelvebfit\scriptscriptfont1=\eightbfit
 \textfont2=\seventeenbsy \scriptfont2=\twelvebsy \scriptscriptfont2=\eightbsy
 \seventeenbf
 \normalbaselineskip=20.736pt\normalbaselines}

\def\fourteenpointbf{%
 \textfont0=\fourteenbf   \scriptfont0=\tenbf   \scriptscriptfont0=\sevenbf
 \textfont1=\fourteenbfit \scriptfont1=\tenbfit \scriptscriptfont1=\sevenbfit
 \textfont2=\fourteenbsy  \scriptfont2=\tenbsy  \scriptscriptfont2=\sevenbsy
 \fourteenbf
 \normalbaselineskip=17.28pt\normalbaselines}

\def\twelvepointbf{%
 \textfont0=\twelvebf   \scriptfont0=\eightbf   \scriptscriptfont0=\sixbf
 \textfont1=\twelvebfit \scriptfont1=\eightbfit \scriptscriptfont1=\sixbfit
 \textfont2=\twelvebsy  \scriptfont2=\eightbsy  \scriptscriptfont2=\sixbsy
 \twelvebf
 \normalbaselineskip=14.4pt\normalbaselines}

\def\tenpointbf{%
 \textfont0=\tenbf   \scriptfont0=\sevenbf   \scriptscriptfont0=\fivebf
 \textfont1=\tenbfit \scriptfont1=\sevenbfit \scriptscriptfont1=\fivebfit
 \textfont2=\tenbsy  \scriptfont2=\sevenbsy  \scriptscriptfont2=\fivebsy
 \tenbf}

%---------------------------------------------------------------------
% main item macros
%---------------------------------------------------------------------

\def\SECTREF#1{\dotfill\csname SR\refmark\romannumeral#1\endcsname\break}
\def\SSECTREF#1{\dotfill\csname SSR\refmark\romannumeral#1\endcsname\break}
\def\NOSECTREF#1{\dotfill ???(#1)\break}
\newlinechar=`\^^J

\def\openauxfile{
  \immediate\openin1\jobname.aux
  \immediate\openout2=hodge-index.aux
  \ifeof1
  \message{^^JCAUTION\string: you MUST run TeX a second time^^J}
  \let\sectref=\NOSECTREF   \let\ssectref=\NOSECTREF  
  \else
  \input \jobname.aux
  \message{^^JCAUTION\string: if the file has just been modified you may 
    have to run TeX twice^^J}
  \let\sectref=\SECTREF    \let\ssectref=\SSECTREF  
  \fi
  \message{to get correct page numbers displayed in the Table of Contents^^J}
  \immediate\openout1=\jobname.aux
  \let\END=\end \def\end{\immediate\closeout1\immediate\closeout2\END}}

\newdimen\itemindent \itemindent=1.5\parindent
\def\smallitem#1{\par\noindent\hangindent0.6667\itemindent%
            \rlap{#1}\kern0.6667\itemindent\ignorespaces}
\def\item#1{\par\noindent\hangindent\itemindent%
            \rlap{#1}\kern\itemindent\ignorespaces}
\def\itemitem#1{\par\noindent\hangindent2\itemindent%
            \kern\itemindent\rlap{#1}\kern\itemindent\ignorespaces}
\def\itemitemitem#1{\par\noindent\hangindent3\itemindent%
            \kern2\itemindent\rlap{#1}\kern\itemindent\ignorespaces}

\def\bottomnote#1#2{\footnote{${}^{#1}$}{{\eightpoint
\baselineskip=9.6pt #2\vskip-9.6pt}}}

\newbox\titlebox   \setbox\titlebox\hbox{\hfil}
\newbox\sectionbox \setbox\sectionbox\hbox{\hfil}
\newcount\fst \fst=1

\def\pagejump{\vfill\eject
  \ifodd\pageno \else 
  {\headline={\hfil}\footline={\hfil}\null\vskip0pt\vfill\eject} \fi
  \fst=\pageno}

\def\pagenumber{\ifnum\pageno<0 \romannumeral-\pageno \else \number\pageno \fi}

\def\folio{\ifnum\pageno=\fst \hfil \else \ifodd\pageno
           {\eightpoint \hfil\copy\sectionbox\hfil{\bf\pagenumber}}\else
           {\eightpoint{\bf\pagenumber}\hfil\copy\titlebox\hfil}\fi\fi}
\headline={\folio}

\def\leftfootline{\fiverm PANORAMAS ET SYNTH\`ESES 3\hfil}
\def\rightfootline{\hfil\fiverm SOCI\'ET\'E MATH\'EMATIQUE DE FRANCE 1996}
\footline={\ifnum\pageno=\fst \hfill \else
  {\ifodd\pageno\rightfootline\else\leftfootline\fi}\fi}

\newcount\numbersection 
\newcount\numbersupersection 
\newcount\numbersubsection
  
\def\blankline{\phantom{}\hfil\vskip0pt}
\def\titlerunning#1|{\setbox\titlebox\hbox{\eightpoint \uppercase{#1}}}
\def\title#1|{\noindent\hfil$\smash{%
              \hbox{\seventeenpointbf #1}}$\hfil
              \titlerunning #1|\medskip
              \numbersection=-1\numbersupersection=0\numbersubsection=0}
\def\titleleft#1|{\noindent$\smash{\hbox{\seventeenpointbf #1}}$\hfil
                  \titlerunning #1|\medskip
                  \numbersection=-1\numbersupersection=0\numbersubsection=0}

\def\supersection#1|{%
  \removelastskip\par\vskip .5cm\penalty -100 
  \vbox{\baselineskip=17.28pt\noindent{{\fourteenpointbf #1}}}
  \vskip3pt
  \penalty 500
  \titlerunning #1|
  \numbersubsection=0
  \advance\numbersupersection by 1
  \immediate\write1{\string\def 
  \string\SSR \refmark\romannumeral\numbersupersection
  \string{%
  \pagenumber\string}}}

\def\sectionrunning#1|{\setbox\sectionbox\hbox{\eightpoint \uppercase{#1}}}
\def\section#1|{%
  \removelastskip\par\vskip .5cm\penalty -100
  \vbox{\baselineskip=14.4pt\noindent{{\twelvepointbf #1}}}
  \vskip2pt
  \penalty 500
  \numbersubsection=0
  \advance\numbersection by 1
  \immediate\write1{\string\def 
  \string\SR \refmark\romannumeral\numbersection
  \string{%
  \pagenumber \string}}
  \sectionrunning#1|}

\def\subsection#1|{%
  \removelastskip\par\vskip .5cm\penalty -100
  \vbox{\noindent{{\tenpointbf #1}}}
  \vskip1pt
  \penalty 500}

\def\writepage{
  \immediate\write1{\string\def 
  \string\page \refmark \string{%
  \pagenumber \string}}}

\def\index#1#2#3{%
  \immediate\write1{\string\def \string\IDX
     #2\refmark\romannumeral#1\string{%
     \noexpand#3 \string\dotfill\ \space
     \refmark, \string\S \number\numbersection, 
     p.\string\ \space\pagenumber\string}}%
  \immediate\write2{\string\IDX #2\refmark\romannumeral#1}}

\long\def\startindex#1{#1}

\catcode`@=11    
\def\cmalign#1{\null\,\vcenter{\normalbaselines\m@th
    \ialign{\hfil$##$&&$##$\hfil\crcr
      \mathstrut\crcr\noalign{\kern-\baselineskip}
      #1\crcr\mathstrut\crcr\noalign{\kern-\baselineskip}}}\,}
\catcode`@=12

\def\boxit#1#2{\hbox{\vrule
 \vbox{\hrule\kern#1
  \vtop{\hbox{\kern#1 #2\kern#1}%
   \kern#1\hrule}}%
 \vrule}}
\def\boxit#1#2{\hbox{#2}}

\long\def\state#1|#2\endstate{\par\vskip 5pt\noindent 
{\bf #1.}\ {\sl #2}\par\vskip 5pt}

\def\preuve{\noindent{\sl Preuve}}

\def\aujourdhui{\number\day\ \ifcase\month\or
janvier\or f{\'e}vrier\or mars\or avril\or mai\or juin\or juillet\or 
ao{\^u}t\or septembre\or octobre\or novembre\or d{\'e}cembre\fi\ \number\year}

\def\bibitem#1&#2&#3&#4&%
{\hangindent=1.66cm\hangafter=1
\noindent\rlap{\hbox{\bf #1}}\kern1.66cm{\rm #2}{\sl #3}{\rm #4.}} 
%---------------------------------------------------------------------
% blackboard symbols
%---------------------------------------------------------------------
\def\bA{{\Bbb A}}
\def\bB{{\Bbb B}}
\def\bC{{\Bbb C}}
\def\bF{{\Bbb F}}
\def\bH{{\Bbb H}}
\def\bK{{\Bbb K}}
\def\bN{{\Bbb N}}
\def\bP{{\Bbb P}}
\def\bQ{{\Bbb Q}}
\def\bR{{\Bbb R}}
\def\bT{{\Bbb T}}
\def\bZ{{\Bbb Z}}
\def\bone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l}
{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}}
%------------------------------------------------------------------
% calligraphic symbols
%------------------------------------------------------------------
\def\cA{{\Cal A}}
\def\cB{{\Cal B}}
\def\cC{{\Cal C}}
\def\cD{{\Cal D}}
\def\cE{{\Cal E}}
\def\cF{{\Cal F}}
\def\cG{{\Cal G}}
\def\cH{{\Cal H}}
\def\cI{{\Cal I}}
\def\cJ{{\Cal J}}
\def\cK{{\Cal K}}
\def\cL{{\Cal L}}
\def\cM{{\Cal M}}
\def\cN{{\Cal N}}
\def\cO{{\Cal O}}
\def\cP{{\Cal P}}
\def\cR{{\Cal R}}
\def\cS{{\Cal S}}
\def\cU{{\Cal U}}
\def\cV{{\Cal V}}
\def\cX{{\Cal X}}
\def\cW{{\Cal W}}
\def\cZ{{\Cal Z}}
%------------------------------------------------------------------
% gothic symbols
%------------------------------------------------------------------
\def\eua{{\euf a}}
\def\eub{{\euf b}}
\def\eug{{\euf g}}
\def\euh{{\euf h}}
\def\eum{{\euf m}}
\def\eup{{\euf p}}
\def\euu{{\euf u}}
\def\euv{{\euf v}}
\def\euS{{\euf S}}
\def\eugl{{\euf g}{\euf l}}
\def\eusl{{\euf s}{\euf l}}
\def\eusu{{\euf s}{\euf u}}
%------------------------------------------------------------------
% special symbols
%------------------------------------------------------------------
\def\ii{{\rm i}}
\def\ee{{\rm e}}
\def\bfp{{\bfit p}}
\def\bfs{{\bfit s}}
\def\numero{n${}^\circ\,$}
\def\newline{\hfill\break}
\def\newpage{\vfill\eject}
\def\olp{{\overline\partial}}
\def\ld{,\,\ldots\,,}
\def\bu{{\scriptstyle\bullet}}
\def\Ll{\langle\!\langle}
\def\Gg{\rangle\!\rangle}
\def\Smark{}
\def\scrvee{{\scriptscriptstyle\vee}}
\def\compact{\subset\!\subset}
\def\ort{\mathrel{\hbox{\vrule width4.0pt height0.4pt depth0pt
                  \vrule width0.4pt height6.0pt depth0pt$\,$}}}
\def\square{{\hfill \hbox{
\vrule height 1.453ex  width 0.093ex  depth 0ex
\vrule height 1.5ex  width 1.3ex  depth -1.407ex\kern-0.1ex
\vrule height 1.453ex  width 0.093ex  depth 0ex\kern-1.35ex
\vrule height 0.093ex  width 1.3ex  depth 0ex}}}
\def\QED{\square}
\def\otL{\mathrel{\mathop{\otimes}\limits^L}}
\def\semidirect{\mathrel{\kern1pt\vrule depth-0.3pt height4.4pt 
\kern-2pt\times\kern-1pt}}
\def\hexnbr#1{\ifnum#1<10 \number#1\else
 \ifnum#1=10 A\else\ifnum#1=11 B\else\ifnum#1=12 C\else
 \ifnum#1=13 D\else\ifnum#1=14 E\else\ifnum#1=15 F\fi\fi\fi\fi\fi\fi\fi}
\def\msatype{\hexnbr\msafam}
\def\msbtype{\hexnbr\msbfam}
\mathchardef\restr="3\msatype16
\mathchardef\ssm="2\msbtype72
\mathchardef\compl="0\msatype7B
\mathchardef\subsetneq="3\msbtype28
\mathchardef\supsetneq="3\msbtype29
\mathchardef\preccurlyeq="3\msatype34
\mathchardef\succcurlyeq="3\msatype3C
\mathchardef\leq="3\msatype36   \let\le\leq
\mathchardef\geq="3\msatype3E   \let\ge\geq

%------------------------------------------------------------------
% displaystyles, hats and tildes and over/underlines
%------------------------------------------------------------------
\let\disp=\displaystyle
\let\scrip=\scriptstyle
\let\ol=\overline
\let\ul=\underline
\def\UL#1{\hbox{$\underline{\hbox{#1}}$}}
\let\wt=\widetilde
\let\wh=\widehat
\def\build#1|#2|#3|{\mathrel{\mathop{\null#1}\limits^{#2}_{#3}}}
%------------------------------------------------------------------
% arrows
%------------------------------------------------------------------
\def\psarrow#1#2#3#4{\special{" 
/arx 2.3 def /ary 2.7 def
/arrow{dup rotate neg exch 0 rlineto 
       arx neg ary rmoveto arx ary neg rlineto arx neg ary neg rlineto} def
0.5 setlinewidth
#1 #2 moveto #3 #4 arrow stroke}}
\def\bignearrow{\hbox{\twelvesy\char"25}}
\def\bigsearrow{\hbox{\twelvesy\char"26}}
\def\bignwarrow{\hbox{\twelvesy\char"2D}}
\def\bigswarrow{\hbox{\twelvesy\char"2E}}
\let\lmapsto=\longmapsto
\let\lra=\longrightarrow
\let\Lra=\Longrightarrow
\def\lhra{\mathrel{\lhook\joinrel\longrightarrow}}
\def\vlra#1|{\mathrel{\hbox to#1mm{\rightarrowfill}}}
\def\vlhra#1|{\mathrel{\lhook\joinrel\hbox to#1mm{\rightarrowfill}}}
\let\Llra=\Longleftrightarrow
\def\lraww{\mathrel{\rlap{$\longrightarrow$}\kern-1pt\longrightarrow}}
\def\dashto{\mathrel{\hbox{
  \kern1pt \vrule height2.45pt depth-2.15pt width2pt}
  \kern1pt{\vrule height2.45pt depth-2.15pt width2pt}
  \kern1pt{\vrule height2.45pt depth-2.15pt width1.7pt\kern-1.7pt}
  {\raise1.4pt\hbox{$\scriptscriptstyle\succ$}}}}
\def\dasharrow{\mathrel{\hbox{
  \kern1pt \vrule height2.45pt depth-2.15pt width2pt}
  \kern1pt{\vrule height2.45pt depth-2.15pt width2pt}
  \kern1pt{\vrule height2.45pt depth-2.15pt width2pt}
  \kern1pt{\vrule height2.45pt depth-2.15pt width1.7pt\kern-1.7pt}
  {\raise1.4pt\hbox{$\scriptscriptstyle\succ$}}}}
\def\vdasharrow{\mathrel{\raise-8pt\hbox{\vbox{\bgroup\baselineskip=3pt
  \hbox{$~$}
  \hbox{\vrule height2pt depth0pt width0.3pt}
  \hbox{\vrule height2pt depth0pt width0.3pt}
  \hbox{\vrule height2pt depth0pt width0.3pt}
  \hbox{\vrule height2pt depth0pt width0.3pt}
  \hbox{\vrule height2pt depth0pt width0.3pt}
  \hbox{\vrule height4pt depth0pt width0.3pt}
  \hbox{\kern-2.75pt\raise2pt\hbox{\smash{$\scriptstyle\vee$}}}
\egroup
}}}}

\def\cu{\hbox{\fivebsy\char'133}}
\def\ca{\hbox{\fivebsy\char'134}}  
\def\hookup{{\lower6.3pt\hbox{\cu}\kern-4.32pt\big\uparrow}}
\def\hookdown{\raise5.3pt\hbox{\ca}\kern-4.32pt\lower3pt\hbox{\big\downarrow}}
%------------------------------------------------------------------
% mathematical operators
%------------------------------------------------------------------
\def\Re{\mathop{\rm Re}\nolimits}
\def\Im{\mathop{\rm Im}\nolimits}
\def\Id{\mathop{\rm Id}\nolimits}
\def\ob{\mathop{\rm ob}\nolimits}
\def\sgn{\mathop{\rm sgn}\nolimits}
\def\Der{\mathop{\rm Der}\nolimits}
\def\res{\mathop{\rm res}\nolimits}
\def\Res{\mathop{\rm Res}\nolimits}
\def\Ker{\mathop{\rm Ker}\nolimits}
\def\Hom{\mathop{\rm Hom}\nolimits} \def\hom{\Hom}
\def\End{\mathop{\rm End}\nolimits}
\def\Aut{\mathop{\rm Aut}\nolimits}
\def\Herm{\mathop{\rm Herm}\nolimits}
\def\U{\mathop{\rm U}\nolimits}
\def\GL{\mathop{\rm GL}\nolimits}
\def\PGL{\mathop{\rm PGL}\nolimits}
\def\SL{\mathop{\rm SL}\nolimits}
\def\SU{\mathop{\rm SU}\nolimits}
\def\Sp{\mathop{\rm Sp}\nolimits}
\def\Sym{\mathop{\rm Sym}\nolimits}
\def\Lie{\mathop{\rm Lie}\nolimits}
\def\Supp{\mathop{\rm Supp}\nolimits}
\def\Ext{\mathop{\rm Ext}\nolimits}
\def\Spec{\mathop{\rm Spec}\nolimits}
\def\Proj{\mathop{\rm Proj}\nolimits}
\def\Vect{\mathop{\rm Vect}\nolimits}
\def\Gr{\mathop{\rm Gr}\nolimits}
\def\codim{\mathop{\rm codim}\nolimits}
\def\limind{\mathop{{\rm lim}\,{\rm ind}}\nolimits}
\def\limproj{\mathop{{\rm lim}\,{\rm proj}}\nolimits}
\def\rg{\mathop{\rm rg}\nolimits}
\def\div{\mathop{\rm div}\nolimits}
\def\ric{\mathop{\rm Ric}\nolimits}
\def\ord{\mathop{\rm ord}\nolimits}
\def\mod{\mathop{\rm mod}\nolimits}
\def\gr{\mathop{\rm Gr}\nolimits}
\def\pr{\mathop{\rm pr}\nolimits}
\def\Op{\mathop{\rm Op}\nolimits}
\def\Psh{\mathop{\rm Psh}\nolimits}
\def\Tr{\mathop{\rm Tr}\nolimits}
\def\Vol{\mathop{\rm Vol}\nolimits}
\def\rang{\mathop{\rm rang}\nolimits}
\def\Jac{\mathop{\rm Jac}\nolimits}
\def\Pic{\mathop{\rm Pic}\nolimits}
\def\Prim{\mathop{\rm Prim}\nolimits}
\def\cHom{\mathop{{\cal H}{\it om}}\nolimits}
%------------------------------------------------------------------
% subscript or superscript operands
%------------------------------------------------------------------
\def\abs{{\rm abs}}
\def\an{{\rm an}}
\def\const{{\rm const}}
\def\loc{{\rm loc}}
\def\hor{{\rm hor}}
\def\nouveau{{\rm nouveau}}
\def\prim{{\rm prim}}
\def\reg{{\rm reg}}
\def\sing{{\rm sing}}
\def\bfD{{\bf D}}
\def\BC{{\rm BC}}
\def\DR{{\rm DR}}
\def\FS{{\rm FS}}
\def\GM{{\rm GM}}
\def\NS{{\rm NS}}
\def\rmO{{\rm 0}}
\def\Dom{{\rm Dom}\,}
\def\Grif{{\rm Grif}}
\def\sep{{\rm sep}}
%------------------------------------------------------------------
% diagrams
%------------------------------------------------------------------
\def\diagram#1{\def\normalbaselines{\baselineskip=0pt\lineskip=5pt}
\matrix{#1}}

\newdimen\unitlength
\unitlength=1mm

\def\Grid{\setbox13=\vbox to 5\unitlength{\hrule width 109mm\vfill}
\setbox13=\vbox to 65mm{\offinterlineskip\leaders\copy13\vfill\kern-1pt\hrule}
\setbox14=\hbox to 5\unitlength{\vrule height 65mm\hfill}
\setbox14=\hbox to 109mm{\leaders\copy14\hfill\kern-2mm\vrule height 65mm}
\ht14=0pt\dp14=0pt\wd14=0pt \setbox13=\vbox to
0pt{\vss\box13\offinterlineskip\box14} \wd13=0pt\box13}
 
\def\grid{\noalign{\Grid}}

\def\arrow(#1,#2)\dir(#3,#4)\long#5{%
\noalign{\leftput(#1,#2){\vector(#3,#4){#5}}}}
 
 
\def\lin(#1,#2)\dir(#3,#4)\long#5{%
\noalign{\leftput(#1,#2){\lline(#3,#4){#5}}}}
 
\def\put(#1,#2)#3{\noalign{\setbox1=\hbox{%
    \kern #1\unitlength
    \raise #2\unitlength\hbox{$#3$}}%
    \ht1=0pt \wd1=0pt \dp1=0pt\box1}}

\newbox\tbox
\newbox\tboxa
 
\def\leftzer#1{\setbox\tbox=\hbox to 0pt{#1\hss}%
     \ht\tbox=0pt \dp\tbox=0pt \box\tbox}
 
\def\rightzer#1{\setbox\tbox=\hbox to 0pt{\hss #1}%
     \ht\tbox=0pt \dp\tbox=0pt \box\tbox}
 
\def\centerzer#1{\setbox\tbox=\hbox to 0pt{\hss #1\hss}%
     \ht\tbox=0pt \dp\tbox=0pt \box\tbox}
 
\def\leftput(#1,#2)#3{\setbox\tboxa=\hbox{%
    \kern #1\unitlength
    \raise #2\unitlength\hbox{\leftzer{#3}}}%
    \ht\tboxa=0pt \wd\tboxa=0pt \dp\tboxa=0pt\box\tboxa}

\def\mapright#1{\mathop{\vbox{\ialign{
                                ##\crcr
    ${\displaystyle\hfil\;\;#1\;\;\hfil}$\crcr
 \noalign{\kern-1pt\nointerlineskip\vskip2.5pt}
    \rightarrowfill\crcr}}\;}}

\def\mapleft#1{\mathop{\vbox{\ialign{
                                ##\crcr
    ${\scriptstyle\hfil\;\;#1\;\;\hfil}$\crcr
    \noalign{\kern-1pt\nointerlineskip}
    \leftarrowfill\crcr}}\;}}


\def\rightput(#1,#2)#3{\setbox\tboxa=\hbox{%
    \kern #1\unitlength
    \raise #2\unitlength\hbox{\rightzer{#3}}}%
    \ht\tboxa=0pt \wd\tboxa=0pt \dp\tboxa=0pt\box\tboxa}
 
\def\centerput(#1,#2)#3{\setbox\tboxa=\hbox{%
    \kern #1\unitlength
    \raise #2\unitlength\hbox{\centerzer{#3}}}%
    \ht\tboxa=0pt \wd\tboxa=0pt \dp\tboxa=0pt\box\tboxa}

\def\rarrow#1#2#3{\smash{\mathop{\hbox to#3{\rightarrowfill}}\limits
^{\scriptstyle#1}_{\scriptstyle#2}}}
 
\def\larrow#1#2#3{\smash{\mathop{\hbox to#3{\leftarrowfill}}\limits
^{\scriptstyle#1}_{\scriptstyle#2}}}
 
\def\darrow#1#2#3{\llap{$\scriptstyle #1$}
\left\downarrow\vbox to#3{}\right.\rlap{$\scriptstyle #2$}}
 
\def\uarrow#1#2#3{\llap{$\scriptstyle #1$}
\left\uparrow\vbox to#3{}\right.\rlap{$\scriptstyle #2$}}
  
\def\vl#1#2#3{\llap{$\scriptstyle #1$}
\left\vert\vbox to#3{}\right.\rlap{$\scriptstyle #2$}}

\def\Vl#1#2#3{\llap{$\scriptstyle #1$}
\left\Vert\vbox to#3{}\right.\rlap{$\scriptstyle #2$}}

\def\hri{\vrule height1.8pt depth-1.4pt width 15mm\kern5pt} 
\def\speci{Foncteurs d\'eriv\'es 
  $\otL$, $R\cHom$, $R\Hom$, $Rf_*$, $Lf^*$, $R\Gamma$}
\def\specii{\hri groupe de cohomologie de De Rham $H^i_\DR(X/k)$}


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