The Stacks project

Typo in limits

Thanks to Laurent Moret-Bailly
https://stacks.math.columbia.edu/tag/01ZT#comment-4056

Slogans by Brian Lawrence edited by Johan de Jong

Thanks to Brian Lawrence

The case of H^0 of Gabbers result

Ample on reduction is ample

move a chapter and rename a chapter

	We moved the chapter "Cohomology of Algebraic Spaces" earlier so
	we can use the results earlier in the treatment of algebraic
	spaces. Also, we finally renamed the chapter "Coherent
	Cohomology" to "Cohomology of Schemes" which is better.

Whitespace changes

LaTeX: \Spec

	Introduced the macro

	\def\Spec{\mathop{\rm Spec}}

	and changed all the occurences of \text{Spec} into \Spec.

LaTeX: fix colim

	Introduced the macro

	\def\colim{\mathop{\rm colim}\nolimits}

	and changed all the occurences of \text{colim} into \colim.

LaTeX: fix lim

	Replaced all the occurences of \text{lim} by \lim or
	\lim\nolimits depending on whether the invocation occured in
	display math or not.

Started tags infrastructure

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

Proof of characterization of affine as image affine under a finite
morphism

	modified:   coherent.tex
	modified:   cohomology.tex
	modified:   limits.tex

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

Finished proof of lemma on image of affines under finite morphisms

	modified:   homology.tex
	modified:   limits.tex

Starting to write proof of finite surjective with source affine has
target affine

	modified:   algebra.tex
	modified:   limits.tex
	modified:   morphisms.tex