The Stacks project

Typo in spaces-properties

LaTeX: \etale

Introduced the macro

\def\etale{{\acute{e}tale}}

and replaced all occurences of \acute{e}tale by \etale

Flat base change of cohomology

	The proof is only sketched so far. We opt for a different proof
	than in the case of schemes. Namely, we want to use Lazard's
	theorem combined with the fact that cohomology commutes with
	filtered colimits on quasi-compact and quasi-separated algebraic
	spaces (which is a good thing to have available anyway).

	Details to follow.

From small to big

	How to pull back modules. This wasn't explicitly stated so we
	added a lemma.

Neurotic changes

	Fix (almost all) complaints of parse.py

End conversion of etale to \'etale.

Etale Cohomology: Functoriality small etale sites

	Almost done with this.

Properties of spaces: A few addtional comments on etale site

Morphisms of algebraic spaces: New file

	Also, some more lemmas on points of algebraic spaces

	modified:   Makefile
	modified:   browse.html
	modified:   preamble.tex
	modified:   scripts/functions.py
	new file:   spaces-morphisms.tex
	modified:   spaces-properties.tex
	modified:   spaces.tex
	modified:   tags/Makefile

Tags: new tags added

	modified:   tags/tags

Properties of spaces: Etale sites and modules on algebraic spaces

	We finally caved in and defined both versions of the etale site
	of an algebraic space. What maybe makes this palatable is the
	little lemma on f-maps showing how to think about the
	relationship between sheaves upstairs and downstairs. Of course
	this lemma holds in some much greater generality, but for now we
	can leave it in this chapter as is.

	Also added some preparatory work on the structure sheaf on an
	algebraic space and quasi-coherent modules. Next up: pushforward
	of quasi-coherent sheaves are sometimes quasi-coherent, right?

	modified:   spaces-properties.tex