%%% -*- latex -*-
%%
%% Copyright (C) 1998, 1999, 2000, 2001, 2006 by Markus Rost.
%% Verbatim copying and distribution is permitted in any medium,
%% provided this notice is preserved.
%%
%% paperD.sty --- for use with AMS-LaTex

%% See also ~/texnix/show-sty.tex

\hyphenation{mani-fold mani-folds semi-sim-ple}
%%% showhyphens:
%% man-i-fold man-i-folds semisim-ple
%% archives generic qua-dratic twisted

%% \leavevmode \textup
%% \itemsep=\bigskipamount \multiply\itemsep2

% \theoremstyle{plain}
% \newtheorem{theorem}{Theorem}
%% theorem without a number
% \newtheorem*{theoremA}{Theorem}
% \newtheorem{lemma}[theorem]{Lemma}
% \newtheorem{corollary}[theorem]{Corollary}
% \newtheorem{proposition}[theorem]{Proposition}

% \theoremstyle{definition}
% \newtheorem{definition}[theorem]{Definition}

% \theoremstyle{remark}
% \newtheorem{remark}[theorem]{Remark}

% \newenvironment{enumerateA}{%
%  \renewcommand{\labelenumi}{\textup{(\theenumi)}}%
%  \renewcommand{\theenumi}{\arabic{enumi}}%
%  \renewcommand{\labelenumii}{\textup{\theenumii)}}%
%  \renewcommand{\theenumii}{\alph{enumii}}%
%  \begin{enumerate}}{\end{enumerate}}

% \numberwithin{theorem}{section}
% \setcounter{tocdepth}{1}

%% For 8pt, 10pt.  And also 12pt.
% F(\mkern-2mu\sqrt[\uproot{1}\leftroot{-1}p]{a})
% F(\mkern-1.5mu{\sqrt[3]{a}})
% F(\mkern-.5mu\sqrt{a})

%% This will allow hyphenation of $p$-dimensional.  It also adds a
%% italic correction.
%\newcommand{\p}{}
%\def\p-{$p\ifdim\fontdimen1\font=0pt\mkern1mu\fi$-\hskip0pt\relax}

%% Some Calligraphic letters
\newcommand{\CA}{\mathcal A}
\newcommand{\CB}{\mathcal B}
\newcommand{\CC}{\mathcal C}
\newcommand{\CalD}{\mathcal D} % problems with \CD
\newcommand{\CE}{\mathcal E}
\newcommand{\CF}{\mathcal F}
\newcommand{\CG}{\mathcal G}
\newcommand{\CH}{\mathcal H}
\newcommand{\CJ}{\mathcal J}
\newcommand{\CK}{\mathcal K}
\newcommand{\CL}{\mathcal L}
\newcommand{\CM}{\mathcal M}
\newcommand{\CN}{\mathcal N}
\newcommand{\CO}{\mathcal O}
\newcommand{\CP}{\mathcal P}
\newcommand{\CR}{\mathcal R}
\newcommand{\CS}{\mathcal S}
\newcommand{\CT}{\mathcal T}
\newcommand{\CU}{\mathcal U}
\newcommand{\CV}{\mathcal V}
\newcommand{\CW}{\mathcal W}
\newcommand{\CX}{\mathcal X}
\newcommand{\CY}{\mathcal Y}
\newcommand{\CZ}{\mathcal Z}

%% bold Letters ("blackboard" letters)
\newcommand{\LA}{\mathbf A}
\newcommand{\LB}{\mathbf B}
\newcommand{\LC}{\mathbf C}
\newcommand{\LF}{\mathbf F}
\newcommand{\LG}{\mathbf G}
\newcommand{\LH}{\mathbf H}
\newcommand{\LJ}{\mathbf J}
\newcommand{\LL}{\mathbf L}
\newcommand{\LN}{\mathbf N}
\newcommand{\LP}{\mathbf P}
\newcommand{\LQ}{\mathbf Q}
\newcommand{\LR}{\mathbf R}
\newcommand{\LS}{\mathbf S}
\newcommand{\LW}{\mathbf W}
\newcommand{\LZ}{\mathbf Z}
\newcommand{\LQZ}{\LQ/\LZ}

%%% Fraktur.  See ~/texnix/look.tex for char numbers.
\DeclareSymbolFont{Fraktur}{U}{euf}{b}{n}
\DeclareMathSymbol{\dA}{\mathalpha}{Fraktur}{"41}
\DeclareMathSymbol{\da}{\mathalpha}{Fraktur}{"61}
\DeclareMathSymbol{\dc}{\mathalpha}{Fraktur}{"63}
%% conflict with \dh
% \DeclareMathSymbol{\dh}{\mathalpha}{Fraktur}{"68}
\DeclareMathSymbol{\dm}{\mathalpha}{Fraktur}{"6D}
\DeclareMathSymbol{\ds}{\mathalpha}{Fraktur}{"73}
%% conflict with \do
% \DeclareMathSymbol{\Do}{\mathalpha}{Fraktur}{"6F}
% \DeclareMathSymbol{\dO}{\mathalpha}{Fraktur}{"4F}
\DeclareMathSymbol{\du}{\mathalpha}{Fraktur}{"75}

%%% Operators and symbols.
%% Usage of Ops: $\GL V$, ${\GL_n}\times\mu_n$.
%% Usage of Ords: $\id\times f$.

\DeclareMathOperator{\ad}{ad} % adjoint
\DeclareMathOperator{\Alt}{Alt}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\Br}{Br}
% \newcommand{\nBr}{\mathop{_n{\rm Br}}\nolimits}
\DeclareMathOperator{\car}{char}
\DeclareMathOperator{\disc}{disc}
\DeclareMathOperator{\Ch}{CH}
\DeclareMathOperator{\coker}{coker}
\DeclareMathOperator{\cor}{cor} % corestriction
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\ed}{ed} % essential dimension
\DeclareMathOperator{\End}{End} % problems with \end
\DeclareMathOperator{\Ext}{Ext}
% \newcommand{\et}{\mathrm{\acute et}} % subscript
\newcommand{\et}{\mathrm{et}} % subscript
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Gal}{Gal}
\newcommand{\Ga}{\LG_{\rm a}}
\newcommand{\Gm}{\LG_{\rm m}}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\image}{im}
\newcommand{\id}{\mathrm{id}}
\DeclareMathOperator{\ind}{ind} % index
\DeclareMathOperator{\Nrd}{Nrd}
\newcommand{\op}{\mathrm{op}} % superscript
\DeclareMathOperator{\Pic}{Pic}
\DeclareMathOperator{\PGL}{PGL}
\DeclareMathOperator{\PGU}{PGU}
\DeclareMathOperator{\PSL}{PSL}
\DeclareMathOperator{\rank}{rank}
\newcommand{\reg}{\mathrm{reg}} % subscript
\DeclareMathOperator{\res}{res} % restriction
\DeclareMathOperator{\SB}{SB} % Severi-Brauer variety
\DeclareMathOperator{\sgn}{sgn} % Signum
\DeclareMathOperator{\SK}{SK} % K-group
\DeclareMathOperator{\SL}{SL}
\DeclareMathOperator{\SO}{SO}
\DeclareMathOperator{\PSO}{PSO}
\DeclareMathOperator{\Proj}{Proj} % projective scheme
\newcommand{\sep}{\mathrm{sep}} % subscript
% \DeclareMathOperator{\Span}{span}
\DeclareMathOperator{\Spec}{Spec}
\DeclareMathOperator{\Spin}{Spin}
\DeclareMathOperator{\trace}{trace}
\DeclareMathOperator{\Trd}{Trd}
\DeclareMathOperator{\trdeg}{tr.deg} % transcendence degree

\newcommand{\amod}{{\rm mod}\mkern5mu} % \bmod with no left argument

\let\tensor\otimes
\newcommand{\inv}{^{-1}}
\newcommand{\dual}{^\vee}

\newcommand{\degre}[2]{[#1\mathbin:#2]}

%% displayed sets
%% \Bmidb only in \displaystyle.
\newcommand{\bmidb}[2]{\{\nonscript\,{#1}\mid{#2}\nonscript\,\}}
\newcommand{\Bmidb}[2]{\left\{\,{#1}\mathrel{\hbox{$
  \displaystyle \mathsurround=0pt \nulldelimiterspace=0pt
  \left|\vphantom{{#1}{#2}}\right.$}}{#2}\,\right\}}

%% Generators and Relations
\newcommand{\amida}[2]{\langle\nonscript\,{#1}\mid{#2}\nonscript\,\rangle}

%% Pfister forms
\newcommand{\pfister}[1]{\langle\!\langle#1\rangle\!\rangle}
\newcommand{\Gpfister}[1]{[[#1]]}
\newcommand{\qform}[1]{\langle#1\rangle}
%% \bot as a binary operator
\newcommand{\orth}{\mathbin\bot}

%% power series
\newcommand{\pseries}[1]{(\mkern-2mu(#1)\mkern-2mu)}
\newcommand{\pseriesr}[1]{[[#1]]}

\newcommand{\metric}[2]{\langle#1,#2\rangle}

%% empty brackets
\newcommand{\emptyform}{\langle\mkern5mu,\mkern2mu\rangle}
\newcommand{\emptylie}{[\mkern6mu,\mkern3mu]}
\newcommand{\emptysymbol}{(\mkern5mu,\mkern2mu)}

%%% left arrows for simplicial sets, two variants.
%% \newcommand{\Lsimpliset}[3]{#1\,\LLarrow\,#2\,\LLLarrow\,#3\,\cdots}
%% \newcommand{\Lsimpliset}[4]{#1\LLarrow#2\LLLarrow#3\LLLLarrow#4\cdots}
%% \newcommand{\LLarrow}{\mathrel{\vcenter{\vbox{\offinterlineskip\Lto\Lto}}}}
%% \newcommand{\LLLarrow}{\mathrel{\vcenter{\vbox{\offinterlineskip\Lto\Lto\Lto}}}}
%% \newcommand{\LLLLarrow}{\mathrel{\vcenter{\vbox{\offinterlineskip\Lto\Lto\Lto\Lto}}}}
%% \newcommand{\Lto}{\hbox{$\leftarrow$}}

%% This is for remarks and reminders
\newcommand{\notfinished}{\centerline{\tt preliminary version}}
%% Why did I put the \leavevmode here?
%\newcommand{\REM}[1]{\leavevmode\marginpar{\tt\raggedright#1}}
\newcommand{\REM}[1]{\marginpar{\tt\raggedright#1}}
%\newcommand{\REM}[1]{\marginpar{\everymath{\scriptstyle}\tt\raggedright#1}}
%\newcommand{\CITE}[2][]{[000]\REM{Citation missing: #1\space#2}}
%\newcommand{\REF}[1]{\REM{Reference missing: #1}}
\newenvironment{typett}{\ttfamily\rightskip 0pt plus100em}{\par}

%% proofitem
% \newcommand{\pitem}{} \def\pitem#1:{#1\enspace\ignorespaces}

%% If \end{proof} does not end the proof
\newcommand{\noqed}{\let\qed\relax}

%% easy going for small 2x2 matrices
\newcommand{\smatrix}[4]{\bigl(\begin{smallmatrix}
   #1&#2\\#3&#4\end{smallmatrix}\bigr)}

%% commutative diagrams.
%% cd-environment: shorter arrows for wide diagrams
%% one optional argument: stretchfactor for longrightarrow
\newenvironment{cd}[1][1]{\setbox0\hbox{$\longrightarrow$}%
  \minCDarrowwidth #1\wd0 \begin{CD}}{\end{CD}}

%% For URLs use empty discretionary breaks after any of :./ except
%% before / ("http://www" can break only after "://").  Inside \myurl,
%% ~ is a normal character and \- is an empty discretionary break
%% (usage: "bie\-le\-feld.de/~rost").
\newcommand{\myurl}{}
\newcommand{\Wdot}{\futurelet\next\WDOT} \newcommand{\WDOT}{.\Wifs}
\newcommand{\Wcolon}{\futurelet\next\WCOLON} \newcommand{\WCOLON}{:\Wifs}
\newcommand{\Wslash}{\futurelet\next\WSLASH} \newcommand{\WSLASH}{/\Wifs}
\newcommand{\Wifs}{\ifx\next\Wslash\else\-\fi}
\newcommand{\Wcats}{\catcode`\.=13 \catcode`\:=13 \catcode`\/=13}
{\Wcats \gdef\myurl{\bgroup \catcode`\~=12 \def\-{\discretionary{}{}{}}%
  \Wcats \let.\Wdot \let:\Wcolon \let/\Wslash \Wmyurl}}
\newcommand{\Wmyurl}[1]{\upshape$\langle$#1$\rangle$\egroup}

%%% end of file
