The Stacks project

Mistake in formula for permutation in cohomology

Thanks to Et
https://stacks.math.columbia.edu/tag/01FM#comment-8368

Chech complexes of unbounded complexes

This is a bit lame... and proofs still need to be added or fleshed out.

Fix signs in section on Cech cohomology of complexes

	The Cech complex of a complex of abelian sheaves F^* has terms

		C^p(U, F^q)

	and p is the first index. Hence the differential, according to
	our general conventions should be

		Cech differential + sign * differential of F^*

	This simplifies many of the calculations. We also added a script
	which checks the signs for the cup-product.

Whitespace changes

Latex: get rid of some overfull boxes

	modified:   algebraic.tex
	modified:   chow.tex
	modified:   coherent.tex
	modified:   cohomology.tex
	modified:   constructions.tex
	modified:   descent.tex
	modified:   desirables.tex
	modified:   divisors.tex
	modified:   etale.tex
	modified:   examples-stacks.tex
	modified:   examples.tex
	modified:   exercises.tex
	modified:   fdl.tex
	modified:   homology.tex
	modified:   hypercovering.tex
	modified:   modules.tex
	modified:   morphisms.tex
	modified:   properties.tex
	modified:   schemes.tex
	modified:   simplicial.tex
	modified:   sites.tex
	modified:   spaces.tex
	modified:   topologies.tex
	modified:   varieties.tex

Started tags infrastructure

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

Slightly more about cohomology

	modified:   cohomology.tex
	modified:   homology.tex
	modified:   injectives.tex
	modified:   sheaves.tex

Sign error nontheless because of difference in numbering in PARI script
than in the text

	modified:   cohomology.tex
	modified:   scripts/second-homotopy.gp

Added a horrible proof of alternating Cech equals Cech.
At least I am absolutely sure that it is correct.
TODO:
	Refer to Serre FAC where he shows that there is a homotpy
	without writing one down.
	Track down an actual reference to a correct homotopy.

	modified:   cohomology.tex
	new file:   scripts/first-homotopy.gp
	new file:   scripts/second-homotopy.gp

Tiny bit more on Cech cohomology
Usual problem of not being able to find a suitable reference for
comparing alternating to Cech maps

	modified:   cohomology.tex