1 %auto-ignore

     1 %auto-ignore

     2 %this ensures the arxiv doesn't try to start TeXing here.

     3 %this ensures the arxiv doesn't try to start TeXing here.

     3 

     4 

     4 \usepackage{amsmath,amssymb,amsfonts}

     5 \usepackage{amsmath,amssymb,amsfonts}

     5 \usepackage{ifpdf}

     6 \usepackage{ifpdf}

     6 

     7 

   120 \newcommand{\lmod}[1]{\leftidx{_{#1}}{\operatorname{mod}}{}}

   121 \newcommand{\lmod}[1]{\leftidx{_{#1}}{\operatorname{mod}}{}}

   121 

   122 

   122 \newcommand{\HC}{\operatorname{Hoch}}

   123 \newcommand{\HC}{\operatorname{Hoch}}

   123 \newcommand{\HH}{\operatorname{HH}}

   124 \newcommand{\HH}{\operatorname{HH}}

   124 

   125 

   126 

   131 

   127 \def\bc{{\mathcal B}}

   132 \def\bc{{\mathcal B}}

   128 

   133 

   129 \newcommand{\into}{\hookrightarrow}

   134 \newcommand{\into}{\hookrightarrow}

   130 \newcommand{\onto}{\twoheadrightarrow}

   135 \newcommand{\onto}{\twoheadrightarrow}