The Stacks project

Clarify stuff on deformations of maps thickenings

Cosmetic change

	Given a named theorem, such as Chevalley's theorem, we now code
	this as

	\begin{theorem}[Chevalley's theorem]
	\label{theorem-chevalley}

	and not as

	\begin{theorem}
	\label{theorem-chevalley}
	(Chevalley's Theorem.)

move a chapter and rename a chapter

	We moved the chapter "Cohomology of Algebraic Spaces" earlier so
	we can use the results earlier in the treatment of algebraic
	spaces. Also, we finally renamed the chapter "Coherent
	Cohomology" to "Cohomology of Schemes" which is better.

Cleanup section formally smooth ring maps

LaTeX: Hom and SheafHom

	Introduced the macros

	\def\Hom{\mathop{\rm Hom}\nolimits}
	\def\SheafHom{\mathop{\mathcal{H}\!{\it om}}\nolimits}

	and replaced all the occurences of \text{Hom} and \textit{Hom}
	with these.

LaTeX: \Spec

	Introduced the macro

	\def\Spec{\mathop{\rm Spec}}

	and changed all the occurences of \text{Spec} into \Spec.

Infinitesimal lifting criterion

	Proof (finally) of the relation between smooth and formally
	smooth morphisms of algebraic spaces.

Bunch of changes

	(1) Starting to write about thickenings of algebraic spaces
	(2) Change Omega^1_{X/S} to Omega_{X/S}
	(3) Introduced universal homeomorphisms for algebraic spaces
	(4) If X ---> Y is a surjective, integral morphism of schemes
	and X is an affine scheme, then Y is an affine scheme
	(4) Topological invariance of the site X_{spaces, etale} of an
	algebraic space X (proof unfinished}

	In order to see that also X_{etale} is a topological invariant
	we (I think) need to prove the following result: If X --> Y is a
	integral, universally injective, surjective morphism of
	algebraic spaces then X is a scheme if and only if Y is a
	scheme. There are two proofs of this result in the literature
	(one by David Rydh and one by Brian Conrad); both reduce the
	result to the Noetherian case by limit arguments. I would
	prefer a more direct argument...

More Morphisms: Edit

	Explain when it is neccesary to have affine test schemes and
	when it is unnecessary.

More Morphisms Spaces: Module of differentials

	Started to write about module of differentials of a morphism of
	algebraic spaces. We want to use it in the discussion of
	formally smooth morphisms.

	This required some preliminary work improving the exposition in
	a few other plaves.

Lifting criterion smoothness using artinian rings

	modified:   algebra.tex
	modified:   more-morphisms.tex
	modified:   morphisms.tex

Forgot to add more-morphisms.tex to tags Makefile
Added new tags to tags/tags

	modified:   tags/Makefile
	modified:   tags/tags

New file more-morphisms.tex to start advanced material on morphisms

	modified:   Makefile
	modified:   algebra.tex
	modified:   browse.html
	modified:   chapters.tex
	modified:   cohomology.tex
	new file:   more-morphisms.tex
	modified:   morphisms.tex
	modified:   preamble.tex
	modified:   scripts/functions.py