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main.tex
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% This LaTeX document needs to be compiled with XeLaTeX.
\documentclass[10pt, oneside, leqno]{book}
\usepackage[utf8]{inputenc}
\usepackage{ucharclasses}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[version=4]{mhchem}
\usepackage{stmaryrd}
\usepackage{graphicx}
\usepackage[export]{adjustbox}
\graphicspath{ {./images/} }
\usepackage{mathrsfs}
\usepackage{hyperref}
\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}
\urlstyle{same}
\usepackage[fallback]{xeCJK}
\usepackage{fontspec}
\usepackage{unicode-math}
\usepackage{tikz-cd}
\usetikzlibrary{decorations.pathmorphing}
\DeclareMathOperator{\coker}{Coker}
\DeclareMathOperator{\colim}{Colim}
\DeclareMathOperator{\im}{Im}
\DeclareMathOperator{\coim}{Coim}
\DeclareMathOperator{\Con}{Con}
\def\set#1{\left\{\,#1\,\right\}}
\input{font}
\title{Cohomology Of Sheaves}
\author{Birger Iversen}
\date{}
%New command to display footnote whose markers will always be hidden
\let\svthefootnote\thefootnote
\newcommand\blfootnotetext[1]{%
\let\thefootnote\relax\footnote{#1}%
\addtocounter{footnote}{-1}%
\let\thefootnote\svthefootnote%
}
%Overriding the \footnotetext command to hide the marker if its value is `0`
\let\svfootnotetext\footnotetext
\renewcommand\footnotetext[2][?]{%
\if\relax#1\relax%
\ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi%
\else%
\if?#1\ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi%
\else\svfootnotetext[#1]{#2}\fi%
\fi
}
\AtEndEnvironment{equation}{\expandafter\label{\Roman{chapter}_\arabic{section}_\arabic{equation}}}
\newtheorem{proposition}[equation]{Proposition}
\AtEndEnvironment{proposition}{\expandafter\label{\Roman{chapter}_\arabic{section}_\arabic{equation}}}
\newtheorem{theorem}[equation]{Theorem}
\AtEndEnvironment{theorem}{\expandafter\label{\Roman{chapter}_\arabic{section}_\arabic{equation}}}
\newtheorem{example}[equation]{Example}
\AtEndEnvironment{example}{\expandafter\label{\Roman{chapter}_\arabic{section}_\arabic{equation}}}
\newtheorem{definition}[equation]{Definition}
\AtEndEnvironment{definition}{\expandafter\label{\Roman{chapter}_\arabic{section}_\arabic{equation}}}
\newtheorem{corollary}[equation]{Corollary}
\AtEndEnvironment{corollary}{\expandafter\label{\Roman{chapter}_\arabic{section}_\arabic{equation}}}
\newtheorem{remark}[equation]{Remark}
\AtEndEnvironment{remark}{\expandafter\label{\Roman{chapter}_\arabic{section}_\arabic{equation}}}
\newtheorem{lemma}[equation]{Lemma}
\AtEndEnvironment{lemma}{\expandafter\label{\Roman{chapter}_\arabic{section}_\arabic{equation}}}
\numberwithin{equation}{section}
\renewcommand{\theequation}{\arabic{section}.\arabic{equation}}
\renewcommand{\thechapter}{\Roman{chapter}\quad}
\renewcommand{\thesection}{\Roman{chapter}.\arabic{section}}
\newcommand{\Sh}{\symfrak{Sh}}
\newcommand{\SH}{\symfrak{Sh}}
\newcommand{\AB}{\symfrak{Ab}}
\let\hom\relax
\let\ker\relax
\DeclareMathOperator{\ker}{Ker}
\DeclareMathOperator{\con}{Con}
\DeclareMathOperator{\cyl}{Cyl}
\DeclareMathOperator{\Coker}{\symscr{C\!oker}}
\DeclareMathOperator{\ext}{Ext}
\DeclareMathOperator{\supp}{supp}
\DeclareMathOperator{\hom}{Hom}
\DeclareMathOperator{\id}{id}
\let\R\relax
\DeclareMathOperator{\R}{\texttt{R}}
\let\L\relax
\newcommand{\aAa}{\symscr{A}}
\newcommand{\bBb}{\symscr{b}}
\newcommand{\cCc}{\symscr{C}}
\newcommand{\dDd}{\symscr{D}}
\newcommand{\eEe}{\symscr{E}}
\newcommand{\fFf}{\symscr{F}}
\newcommand{\gGg}{\symscr{G}}
\newcommand{\iIi}{\symscr{I}}
\newcommand{\oOo}{\symscr{O}}
\newcommand{\AAA}{\symfrak{A}}
\newcommand{\BBB}{\symfrak{B}}
\newcommand{\III}{\symfrak{I}}
\newcommand{\AaA}{\symcal{A}}
\newcommand{\BbB}{\symcal{B}}
\newcommand{\CcC}{\symcal{C}}
\newcommand{\DdD}{\symcal{D}}
\newcommand{\IiI}{\symcal{I}}
\newcommand{\JjJ}{\symcal{J}}
\newcommand{\MmM}{\symcal{M}}
\newcommand{\KkK}{\symcal{K}}
\newcommand{\OoO}{\symcal{O}}
\newcommand{\PpP}{\symcal{P}}
\newcommand{\RrR}{\symcal{R}}
\newcommand{\UuU}{\symcal{U}}
\newcommand{\WwW}{\symcal{W}}
\newcommand{\QqQ}{\symcal{Q}}
\newcommand{\XxX}{\symcal{X}}
\newcommand{\YyY}{\symcal{Y}}
\newcommand{\ZzZ}{\symcal{Z}}
\begin{document}
\maketitle
\input{O.tex}
\tableofcontents
\chapter{Homological Algebra}
\input{I}
\chapter{Sheaf Theory}
\input{II}
\chapter{Cohomology with Compact Support}
\input{III.tex}
\chapter{Cohomology and Analysis}
\input{IV.tex}
\chapter{Duality with Coefficient in a Field}
\input{V.tex}
\chapter{Poincare Duality with General Coefficients}
\input{VI.tex}
\chapter{Direct Image with Proper Support}
\input{VII.tex}
\chapter{Characteristic Classes}
\input{VIII.tex}
\chapter{Borel Moore Homology}
\input{IX.tex}
\chapter{Application to Algebraic Geometry}
\input{X.tex}
\chapter{Derived Categories}
\input{XI.tex}
\end{document}