The Stacks project

Check flatness in flat base change

Thanks to Du
https://stacks.math.columbia.edu/tag/02KH#comment-5458

Remove double text

Thanks to Nicolas Müller
https://stacks.math.columbia.edu/tag/02KH#comment-4682

Typo

THanks to Daniel
http://stacks.math.columbia.edu/tag/02KH#comment-2343

Corrected typos in coherent.tex

Base change by finite locally free

Thanks to Ofer Gabber who writes:

Base change for quasi-coherent cohomology holds for a finite field
extension without the qcqs assumption, more generally if  the ring
map R---->R' is s.t. R' is a f.g. projective R-module, X is
an R-scheme, F a quasi-coherent sheaf on X, X' &F' the base changes
to R', then for all  p ,
H^p(X,F) tensor (over R) R'   maps isomorphically to H^p(X',F').

Improve statement flat base change

Most references using this lemma use the case where the bases
are affine so it makes sense to state this case in the lemma.

Fix typos

Thanks to correction_bot
Online comments 931 -- 936

\text{Spec} ---> \Spec

Cohomology and base change

	Cleaned up and hopefully easier to read.

Fixed nonsensical lemma in homology.tex
Added info on the base change map
Added reformulation of hypercoverings of topological spaces
Added flat morphisms of ringed spaces to modules.tex

	modified:   coherent.tex
	modified:   cohomology.tex
	modified:   homology.tex
	modified:   hypercovering.tex
	modified:   modules.tex

Added new tags to the file tags/tags

	modified:   tags/tags

Cohomolgoy and base change improved
Changed corresponding tags in tags/tags
Added more variants of etale localizing quasi-finite maps
Started section on structure of quasi-finite maps
Improved section on proper morphisms
Improved section on integra; and finite morphisms
Characterizing integral morphisms as universally closed and affine
Comment added to section on proper maps in topology

	modified:   coherent.tex
	modified:   more-morphisms.tex
	modified:   morphisms.tex
	modified:   schemes.tex
	modified:   tags/tags
	modified:   topology.tex