The Stacks project

Codimension 0 points on algebraic spaces

This is a rather large set of changes all related to different ways of
saying what it means to have a ``generic point'' on an algebraic space.
One particularly nice lemma says that an algebraic space which locally
(in a suitable sense) has finitely many generic points is automatically
a reasonable algebraic space (in particular decent). The proof is the
same as the argument showing that a decent locally Noetherian algebraic
space is quasi-separated.

These types of results may be useful in the future as tools to decide
whether a given algebraic space is decent and/or quasi-separated.

Tags: added new tags

Properties of Spaces: Dimension

	Introduced the notion of the dimension of an algebraic space at
	a point. We do not use the topological space |X| for this,
	instead we use the dimension of an etale cover by a scheme.

	We also prove a lemma on the invariance of dimension of local
	rings under etale extensions, leading also to the equality of
	the dimension of a local ring and its henselization.