The Stacks project

Split out arguments in proof smooth base change

I decided to leave in the very long proof because it seems that for some
people this may be easier to read than the version with all the
references to the lemmas building up the proof.

Also added: some more cases where the base change maps are isomorphisms
on sheaves.

More standard use of "partial ordering"

Thanks to Wei Xu
http://stacks.math.columbia.edu/tag/00CR#comment-588
and to Keenan Kidwell
http://stacks.math.columbia.edu/tag/00D3#comment-2102

More standard use of "partial ordering"

Thanks to Wei Xu
http://stacks.math.columbia.edu/tag/00CR#comment-588
and to Keenan Kidwell
http://stacks.math.columbia.edu/tag/00D3#comment-2102

Minor corrections on algebra matters.

algebra.tex:355: The "this" in the "Informally this means..." paragraph
refers to the notion of "finitely presented", and so belongs inside part (2) of the
definition, rather than after it. (Otherwise it should be more explicit
about what it means by "this".)

algebra.tex:718: I have never seen transitive relations referred to as
"associative", so I take this for a typo.

algebra.tex:1863: There are various R-modules around, so I figured a bit more
explicitness wouldn't hurt.

algebra.tex:2021: It is certainly not the only iso $f : S^{-1}R \otimes_R M
\to S^{-1}M$.

algebra.tex:8067: The "(faithfully)" alternatives were added to the second
sentence to help prove the first sentence. It wouldn't hurt splitting the
lemma in two, though, as it now makes four different claims.

more-algebra.tex:4556: Fixed to the best of my knowledge. I am not 100% sure
of this since I don't know your notations.

Add section on colimits to algebra.tex

Started tags infrastructure

	new file:   scripts/add_tags.py
	modified:   scripts/functions.py
	new file:   tags/initial_tags
	new file:   tags/tags

List of changes:
	Improved exposition colimits modules in algebra.tex
	Fixed typo on categories.tex
	Proof basic lemma cohomology P^n_R, R Noetherian
	Characterize affines by vanishing cohomology
	Cohmology commutes with directed colimits sometimes
	Typos constructions.tex
	Clarify quasi-affine section
	Ideals directed limit finite type ideals
	Characterize affines in properties.tex
	Closed points exist in quasi-compact spaces

	modified:   algebra.tex
	modified:   categories.tex
	modified:   coherent.tex
	modified:   cohomology.tex
	modified:   constructions.tex
	modified:   limits.tex
	modified:   modules.tex
	modified:   properties.tex
	modified:   topology.tex

More neurotic changes

Added section on tensor product by Fraser Hiu

	modified:   CONTRIBUTORS
	modified:   algebra.tex