The Stacks project

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.

Separation conditions on algebraic spaces

	As requested by David Rydh we replaced the notion of ``weakly
	locally separated'' and replaced it by ``locally separated''.
	We added remarks to the effext that in most of the literature in
	existence the term ``locally separated'' also implies
	quasi-separated, allthough we do not require this.

Properties of Spaces: Quasi-separated spaces and fpqc topology

	A Zariski locally quasi-separated space satisfies the sheaf
	condition for the fpqc topology.

Properties of Spaces

	We started to work out the suggestion in commit 2100745. In fact
	the suggestion was wrong and the correct notion is to require
	that there exists a surjective etale morphism \coprod U_i --> X
	such that for each i the two projection morphisms
		U_i \times_X U_i --> U_i
	are quasi-compact. We are calling such an algebraic space
	``reasonable''. If you do not like this please complain soon.
	Sofar the only interesting observation is that points on
	reasonable spaces are represented by monomorphisms from spectra
	of fields. We also expect that valuative criteria will work well
	for reasonable algebraic spaces.

Properties of spaces: Points of quasi-separated spaces behave well

	modified:   morphisms.tex
	modified:   schemes.tex
	modified:   spaces-properties.tex

Tags: added new tags to the project

	modified:   tags/tags

Collection of small changes

	Small addition in algebra.tex
	Invariant opens, representable quotients in groupoids
	Finite monomorphism of schemes is closed immersion
	Separation axioms added to spaces-properties
	Morphism between algebraic spaces is representable by algebraic
		spaces

	modified:   algebra.tex
	modified:   groupoids.tex
	modified:   morphisms.tex
	modified:   spaces-properties.tex
	modified:   spaces.tex