The Stacks project

Final in series nuerotic edits

LaTeX: \Sch

	Introduced a new macro

	\def\Sch{\textit{Sch}}

	and replaced all the occurences of \textit{Sch} with \Sch.

LaTeX: \Spec

	Introduced the macro

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

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

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...

Begin translating etale to \'etale or \acute{e}tale (in Math mode).

Etale Cohomology: \'etale ---> etale

	Sorry to all french people!

Small random collection of changes

Etale Cohomology: Introducing tau-sites

	There seems to be no way around actually introducing the
	tau-sites in the chapter on etale cohomology. As a result we
	noticed something missing in the chapter on topologies, namely
	the statement that the topologies on the big (absolute)
	tau-sites are induced from the corresponding toplogies on the
	category of all schemes. We added this also.

Etale Cohomology: Remove the fpqc site

	Explanation can be found in the text,

Tags: Added new tags

	Mainly new tags for lemmas/propositions/theorems in the chapter
	on etale cohomology.

Etale Cohomology: White space changes only

Etale COhomology: More edits

	Coding style...

Etale Cohomology: Added it to the project and more edits

	A solution to the problem mentioned in the previous commit may
	be to add parts of the Chapter as Appendices maybe in a smaller
	font. Still not sure.

Etale Cohomology: Added it to the project and more edits

	A solution to the problem mentioned in the previous commit may
	be to add parts of the Chapter as Appendices maybe in a smaller
	font. Still not sure.

Etale Cohomology: Lots of edits

	One of the problems is that the coding style is completely
	different and nonuniform. Another is that there is a lot of
	material for which it will not be possible to find proofs
	internally in the stacks project for a long time. Perhaps we
	need to introduce a way of indicating this in the document.

	A better solution is perhaps to add only those parts to the
	actual stacks book published on the web which mesh well with
	the stacks project.

CONTRIBUTORS: Added Min Lee

	See previous commit

Etale Cohomology: Lecture notes from a course

	Taken by Thibaut Pugin, Zachary Maddock and Min Lee (in reverse
	alphabetical ordering).

	Fall 2009 Mathematics G6289 section 001
	ALGEBRAIC GEOMETRY

	The topic was etale cohomology of schemes. The intent was to
	work through the chapters [Arcata] and [Rapport] of SGA 4 1/2.
	The class met Tuesday and Thursday from 11-12:15 in Room 307 of
	the Mathematics Building.