The Stacks project

Make notation for modules on stacks more uniform

It is possible that these changes make the problem worse!

QCoh = Ind Coh on Noetherian Alg Stacks

Improvements handling qcoh stuff on stacks

LaTeX

Introduced a new macro

\def\Coker{\text{Coker}}

and replaced all occurrences of \text{Coker} by \Coker

LaTeX

Introduced a macro

\def\Ker{\text{Ker}}

and replace all occurrences of \text{Ker} with \Ker

LaTeX

Introduced a macro

\def\QCoh{{\textit{QCoh}}}

and replaced almost all occurences of \textit{QCoh} by \QCoh. There are
still some places where we use \textit{QCoh}, namely in the chapter
on examples of stacks. This is because the meaning there is different;
it indicates a category fibred in groupoids over Sch and not the notational
gadget that takes a ringed topos and spits out its category of
quasi-coherent modules.

LaTeX: \etale

Introduced the macro

\def\etale{{\acute{e}tale}}

and replaced all occurences of \acute{e}tale by \etale

Split chapter Cohomology of Stacks; added new chapter

Reason: Same structure as for schemes and spaces
New chapter added to the project
Filename: stacks-perfect.tex
Title: Derived Categories of Stacks

TAGS: Added new tags

QCoh on lisse-etale is weak serre

	The proof of this is now finally done. What's more important is
	that we have finally proved the result that is going to be a key
	ingredient later on, namely that Lg_!H with H quasi-coherent on
	the lisse-etale site) is a complex whose cohomology sheaves are
	locally quaasi-coherent and have the flat base change property.
	Essentially this is saying the following: Given a ring A and a
	module M the functor

		B |---> Tor_p^A(B, M)

	is locally quasi-coherent and has the flat base change property.
	This is obvious as these Tor groups can be computed using a
	fixed free resolution of M.

Quasi-coherent modules on X_{lisse,etale} form a weak Serre subcategory

	Of course we've seen this before (in some sense) but it is fun
	to deduce it from the earlier results. Proof not completely
	finished. Probably it would be better to repeat the proof from
	the chapter "sheaves on stacks".