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% Choose between print and web versions | ||
\def\mode{PrintMode} | ||
\def\WebMode{% | ||
\documentclass[a4paper,oneside,fleqn]{book} | ||
\usepackage{geometry} | ||
} | ||
\def\PrintMode{% | ||
\documentclass[twoside,fleqn]{book} | ||
\usepackage[paperwidth=15.6cm, paperheight=23.4cm]{geometry} | ||
} | ||
\csname\mode\endcsname | ||
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% Preamble | ||
\usepackage{ifthen} % some settings in the preamble depend on PrintMode vs WebMode | ||
\input{preamble} | ||
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% Design | ||
\usepackage{Baskervaldx} | ||
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% Bibliography | ||
\addbibresource{fga-bibliography.bib} | ||
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% Metadata | ||
\title{Foundations of Algebraic Geometry} | ||
\author{Alexander Grothendieck} | ||
\date{1956--1962} | ||
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% Document | ||
\begin{document} | ||
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\frontmatter | ||
\pagestyle{plain} | ||
\maketitle | ||
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\begin{abstract} | ||
This is an English translation of {Alexander Grothendieck}'s "Fondements de la Géometrie Algébrique". | ||
The original (French) notes have been scanned and uploaded by the Grothendieck Circle, though you can also find the individual talks, as well as the errata, at \url{www.numdam.org/actas/SB/}. | ||
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The translator (\href{https://thosgood.com}{Tim Hosgood}) takes full responsibility for any errors introduced, and claims no rights to any of the mathematical content herein. | ||
Any notes by the translator are in italics and prefixed with "[Trans.]". | ||
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You can view the entire source code of this translation (and contribute or submit corrections) in the GitHub repository \url{github.com/thosgood/fga/}. | ||
Corrections and comments welcome. | ||
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The translator would like to sincerely thank Steve Hnizdur for catching many typos and mistakes. | ||
\end{abstract} | ||
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\setcounter{tocdepth}{1} | ||
\tableofcontents | ||
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\mainmatter | ||
\pagestyle{fancy} | ||
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% Foreword | ||
\setcounter{part}{-1} | ||
\renewcommand\thepart{} | ||
\include{fga-foreword} | ||
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% FGA 1 | ||
\renewcommand\thepart{\arabic{part}} | ||
\include{fga1} | ||
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% FGA 2 | ||
\setcounter{chapter}{0} | ||
\include{fga2} | ||
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% FGA 3 | ||
\part{Technique of descent and existence theorems in algebraic geometry} | ||
\setcounter{part}{0} | ||
\renewcommand\thepart{3.\Roman{part}} | ||
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% FGA 3.I | ||
\setcounter{chapter}{0} | ||
\renewcommand\thechapter{\Alph{chapter}} | ||
\renewcommand\thesubsection{\alph{subsection}} | ||
\include{fga3.i} | ||
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% FGA 3.II | ||
\setcounter{chapter}{0} | ||
\include{fga3.ii} | ||
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% FGA 3.III | ||
\setcounter{chapter}{-1} | ||
\renewcommand\thechapter{\arabic{chapter}} | ||
\include{fga3.iii} | ||
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% FGA 3.IV | ||
\setcounter{chapter}{-1} | ||
\include{fga3.iv} | ||
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% FGA 3.V | ||
\setcounter{chapter}{0} | ||
\include{fga3.v} | ||
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% FGA 3.VI | ||
\setcounter{chapter}{-1} | ||
\include{fga3.vi} | ||
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% Bibliography | ||
\backmatter | ||
\nocite{*} | ||
\pagestyle{plain} | ||
\printbibliography[heading=bibintoc,title=Bibliography] | ||
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\end{document} |
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%!TEX root = main.tex | ||
\usepackage[T1]{fontenc} | ||
\usepackage[final]{microtype} | ||
\usepackage{amsmath,amssymb} | ||
\usepackage{amsthm,mathtools} | ||
\usepackage{amscd} | ||
\usepackage{etoolbox} | ||
\usepackage[cal=esstix,scr=rsfs]{mathalfa} | ||
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% DOUBLE QUOTES | ||
\usepackage[autostyle=false,style=english]{csquotes} | ||
\MakeOuterQuote{"} | ||
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% HEADERS AND FOOTERS | ||
\usepackage{fancyhdr} | ||
\renewcommand{\chaptermark}[1]{\markboth{\thechapter. #1}{}} | ||
\renewcommand{\sectionmark}[1]{\markboth{\thesection. #1}{}} | ||
\fancyhf{} | ||
\ifthenelse{\equal{\mode}{WebMode}}{% | ||
\fancyhead[C]{\small FGA~\thepart\\\leftmark}% | ||
\renewcommand{\headrulewidth}{0.5pt}% | ||
}{% | ||
\fancyhead[LO]{FGA~\thepart}% | ||
\fancyhead[RE]{\leftmark}% | ||
\renewcommand{\headrulewidth}{0pt}% | ||
} | ||
\fancyfoot[C]{\thepage} | ||
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% BIBLIOGRAPHY | ||
\usepackage[backend=bibtex]{biblatex} | ||
\renewbibmacro{in:}{% | ||
\ifboolexpr{% | ||
test {\ifentrytype{article}}% | ||
}{}{\printtext{\bibstring{in}\intitlepunct}}% | ||
} | ||
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% LINKS | ||
\ifthenelse{\equal{\mode}{WebMode}}{% | ||
\usepackage{xcolor}% | ||
\usepackage[colorlinks=true,linkcolor={blue!60!black},citecolor={blue!60!black},urlcolor={purple!60!black}]{hyperref}% | ||
}{% | ||
\usepackage[colorlinks=false,hidelinks]{hyperref} | ||
} | ||
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\usepackage[nameinlink,capitalize]{cleveref} | ||
\crefname{section}{§}{§§} | ||
\crefname{subsection}{§}{§§} | ||
\labelformat{subsection}{\thesection.#1} | ||
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% HEADINGS | ||
\usepackage{titlesec} | ||
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\titleformat{\part}[display]{}{\huge FGA~\thepart}{8pt}{\huge} | ||
\titleclass{\part}{top} | ||
\titlespacing{\part}{0pt}{0pt}{*6} | ||
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\titleformat{\chapter}[hang]{}{\Large\thechapter.}{8pt}{\Large} | ||
\ifthenelse{\equal{\mode}{WebMode}}{% | ||
\titleclass{\chapter}{straight}% | ||
\titlespacing{\chapter}{0pt}{*8}{*4}% | ||
}{% | ||
\titlespacing{\chapter}{0pt}{0pt}{*4}% | ||
} | ||
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\titleformat{\section}[hang]{}{\large\thesection.}{8pt}{\large} | ||
\titlespacing{\section}{0pt}{*8}{*2} | ||
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\titleformat{\subsection}[hang]{}{\large\thesection.\thesubsection.}{8pt}{\large} | ||
\titlespacing{\subsection}{0pt}{*8}{*2} | ||
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% ENVIRONMENTS | ||
\makeatletter | ||
\def\skipsinglepar{% | ||
\@ifnextchar\par | ||
{\expandafter\skipsinglepar\@gobble}% | ||
{}% | ||
} | ||
\makeatother | ||
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%% Abstract | ||
\newenvironment{abstract}{\par\vspace{\topsep}\noindent\textbf{Note from the translator.}~}{\par\vspace{\topsep}} | ||
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%% Numbering for \ref | ||
\makeatletter | ||
\newcommand{\setnumber}[1]{\def\@currentlabel{#1}} | ||
\makeatother | ||
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%% Numbered equations | ||
\newenvironment{eqn}[1]{\vspace{-1em}}{} | ||
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%% Original citations | ||
\newenvironment{original}{\par\vspace{\topsep}\hrule\vspace{\topsep}\noindent}{\vspace{\topsep}\hrule\par\vspace{\topsep}} | ||
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%% Custom inner environment | ||
\newenvironment{inenv}[4][]{% | ||
% first argument (optional) is the title | ||
% second argument (mandatory) is the number | ||
% third argument (mandatory) is the taxon | ||
% fourth argument (mandatory) is empty for non-italic | ||
\par\vspace{\topsep}\noindent% | ||
\ifstrempty{#2}{%if no number | ||
\ifstrempty{#1}{%if no title | ||
\textbf{#3.}% | ||
}{%if title | ||
\textbf{#3} (#1).% | ||
}% | ||
}{%if number | ||
\ifstrempty{#1}{% | ||
\textbf{#3~#2.}% | ||
}{% | ||
\textbf{#3~#2} (#1).% | ||
}% | ||
}% | ||
\ifstrempty{#4}{}{\itshape}~}%non-italic | ||
{\par\vspace{\topsep}} | ||
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%% Italicised environments | ||
\newenvironment{theorem}[2][]% | ||
{\begin{inenv}[#1]{#2}{Theorem}{italic}}% | ||
{\end{inenv}} | ||
\newenvironment{lemma}[2][]% | ||
{\begin{inenv}[#1]{#2}{Lemma}{italic}}% | ||
{\end{inenv}} | ||
\newenvironment{proposition}[2][]% | ||
{\begin{inenv}[#1]{#2}{Proposition}{italic}}% | ||
{\end{inenv}} | ||
\newenvironment{corollary}[2][]% | ||
{\begin{inenv}[#1]{#2}{Corollary}{italic}}% | ||
{\end{inenv}} | ||
\newenvironment{statement}[2][]% | ||
{\begin{inenv}[#1]{#2}{Statement}{italic}}% | ||
{\end{inenv}} | ||
\newenvironment{conjecture}[2][]% | ||
{\begin{inenv}[#1]{#2}{Conjecture}{italic}}% | ||
{\end{inenv}} | ||
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%% Upright environments | ||
\newenvironment{definition}[2][]% | ||
{\begin{inenv}[#1]{#2}{Definition}{}}% | ||
{\end{inenv}} | ||
\newenvironment{remark}[2][]% | ||
{\begin{inenv}[#1]{#2}{Remark}{}}% | ||
{\end{inenv}} | ||
\newenvironment{remarks}[2][]% | ||
{\begin{inenv}[#1]{#2}{Remarks}{}}% | ||
{\end{inenv}} | ||
\newenvironment{example}[2][]% | ||
{\begin{inenv}[#1]{#2}{Example}{}}% | ||
{\end{inenv}} | ||
\newenvironment{scholium}[2][]% | ||
{\begin{inenv}[#1]{#2}{Scholium}{}}% | ||
{\end{inenv}} |