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.

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.

Whitespace changes

Tags: Added new tags

Fixes in spaces-properties.tex

	We tried to find arguments for some of the previous results in
	the quasi-separated case which are easier than the original more
	general ones. We only partially succeeded. But on the other
	hand, we can in the future keep simplifying this chapter and add
	the more involved arguments to the chapter on decent spaces.