The Stacks project

Move a section earlier

Fix references and tag

LaTeX: \etale

Introduced the macro

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

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

Move parasitic modules material

	From the chapter on adequate modules to the chapter on descent.
	At this point there are no longer any references to the adequate
	modules chapter, so we can move it later...

Cohomology of unbounded complexes

	The case of sheaves on sites. Exactly the same as in the case of
	sheaves of modules on spaces.

Comparison

	Extremely boring comparison result between big and small sites
	of schemes and for algebraic stacks representable by algebraic
	spaces. Still preparing for a discussion of cohomology of
	quasi-coherent sheaves on algebraic stacks.

Fix reference

LaTeX: \Sch

	Introduced a new macro

	\def\Sch{\textit{Sch}}

	and replaced all the occurences of \textit{Sch} with \Sch.

Tags: Added new tags

Comparison derived cats

	Ok, so although the proofs are a bit sketchy and use unbounded
	derived functors we haven't introduced yet, it seems quite clear
	that the category D_{QCoh}(X) is the quotient of the category
	D_{Adeq}(X) by the subcategory D_C(X) where C is the category of
	parasitic adequate modules. This is cool, because it gives a
	construction of the derived category D_{QCoh}(X) entirely in
	terms of the derived category of O-modules on the big fppf site
	of the scheme X.