New chapter entitled "Flatness on Algebraic Spaces"

Makefile

@@ -21,7 +21,7 @@ LIJST = introduction conventions sets categories \
 	spaces-cohomology spaces-limits spaces-divisors spaces-over-fields \
 	spaces-topologies \
 	spaces-descent spaces-perfect spaces-more-morphisms spaces-pushouts \
-	spaces-groupoids spaces-more-groupoids bootstrap \
+	spaces-flat spaces-groupoids spaces-more-groupoids bootstrap \
 	groupoids-quotients spaces-simplicial formal-spaces restricted \
 	spaces-resolve \
 	formal-defos defos cotangent \

chapters.tex

@@ -79,13 +79,14 @@
 \item \hyperref[spaces-perfect-section-phantom]{Derived Categories of Spaces}
 \item \hyperref[spaces-more-morphisms-section-phantom]{More on Morphisms of Spaces}
 \item \hyperref[spaces-pushouts-section-phantom]{Pushouts of Algebraic Spaces}
+\item \hyperref[spaces-flat-section-phantom]{Flatness on Algebraic Spaces}
 \item \hyperref[spaces-groupoids-section-phantom]{Groupoids in Algebraic Spaces}
 \item \hyperref[spaces-more-groupoids-section-phantom]{More on Groupoids in Spaces}
 \item \hyperref[bootstrap-section-phantom]{Bootstrap}
 \end{enumerate}
 Topics in Geometry
 \begin{enumerate}
-\setcounter{enumi}{68}
+\setcounter{enumi}{69}
 \item \hyperref[groupoids-quotients-section-phantom]{Quotients of Groupoids}
 \item \hyperref[spaces-simplicial-section-phantom]{Simplicial Spaces}
 \item \hyperref[formal-spaces-section-phantom]{Formal Algebraic Spaces}
@@ -94,14 +95,14 @@
 \end{enumerate}
 Deformation Theory
 \begin{enumerate}
-\setcounter{enumi}{73}
+\setcounter{enumi}{74}
 \item \hyperref[formal-defos-section-phantom]{Formal Deformation Theory}
 \item \hyperref[defos-section-phantom]{Deformation Theory}
 \item \hyperref[cotangent-section-phantom]{The Cotangent Complex}
 \end{enumerate}
 Algebraic Stacks
 \begin{enumerate}
-\setcounter{enumi}{76}
+\setcounter{enumi}{77}
 \item \hyperref[algebraic-section-phantom]{Algebraic Stacks}
 \item \hyperref[examples-stacks-section-phantom]{Examples of Stacks}
 \item \hyperref[stacks-sheaves-section-phantom]{Sheaves on Algebraic Stacks}
@@ -118,7 +119,7 @@
 \end{enumerate}
 Miscellany
 \begin{enumerate}
-\setcounter{enumi}{89}
+\setcounter{enumi}{90}
 \item \hyperref[examples-section-phantom]{Examples}
 \item \hyperref[exercises-section-phantom]{Exercises}
 \item \hyperref[guide-section-phantom]{Guide to Literature}

preamble.tex

@@ -114,6 +114,7 @@
 \externaldocument[spaces-perfect-]{spaces-perfect}
 \externaldocument[spaces-more-morphisms-]{spaces-more-morphisms}
 \externaldocument[spaces-pushouts-]{spaces-pushouts}
+\externaldocument[spaces-flat-]{spaces-flat}
 \externaldocument[spaces-groupoids-]{spaces-groupoids}
 \externaldocument[spaces-more-groupoids-]{spaces-more-groupoids}
 \externaldocument[bootstrap-]{bootstrap}

spaces-flat.tex

@@ -0,0 +1,45 @@
+\input{preamble}
+
+% OK, start here.
+%
+\begin{document}
+
+\title{Flatness on Algebraic Spaces}
+
+\maketitle
+
+\phantomsection
+\label{section-phantom}
+
+\tableofcontents
+
+
+
+\section{Introduction}
+\label{section-introduction}
+
+\noindent
+In this chapter, we discuss some advanced results on flat modules and
+flat morphisms in the setting of algebraic spaces. We strongly encourage
+the reader to take a look at the corresponding
+chapter in the setting of schemes first, see
+More on Flatness, Section \ref{flat-section-introduction}.
+A reference is the paper \cite{GruRay} by Raynaud and Gruson.
+
+
+
+
+
+
+
+
+
+
+
+\input{chapters}
+
+
+\bibliography{my}
+\bibliographystyle{amsalpha}
+
+\end{document}

tags/Makefile

@@ -22,7 +22,7 @@ LIJST = introduction conventions sets categories \
 	spaces-cohomology spaces-limits spaces-divisors spaces-over-fields \
 	spaces-topologies \
 	spaces-descent spaces-perfect spaces-more-morphisms spaces-pushouts \
-	spaces-groupoids spaces-more-groupoids bootstrap \
+	spaces-flat spaces-groupoids spaces-more-groupoids bootstrap \
 	groupoids-quotients spaces-simplicial formal-spaces restricted \
 	spaces-resolve \
 	formal-defos defos cotangent \