The Stacks project

More on Noetherian algebraic spaces

	For a Moetherian algebraic space X the space |X| is sober and
	Noetherian.

Descent on Spaces: Lemma on types of morphisms fpqc local on the base

Noetherian Algebraic Spaces

	We changed the definition of a Noetherian algebraic space. We
	now require in addition to being locally Noetherian and
	quasi-compact also that it be quasi-separated. As David Rydh
	puts it:

	"This is motivated by the fact that noetherian spaces should be
	as nice as possible and by the fact that on such spaces we have
	that every quasi-coherent sheaf is the limit of finitely
	presented sheaves (=coherent sheaves). Also, you should not
	worry about the fact that oetherian and X --> Y of finite type
	does not imply X noetherian but instead require finite
	presentation (just as in my definition of pseudo-noetherian)."

TAGS: added new tags

	modified:   tags/tags

Properties of spaces: Add some simple definitions

	modified:   spaces-properties.tex