The Stacks project

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.

Spell check: words starting with d, e, f, g, D, E, F, or G

Move a section

Moved the section on derived categories of quasi-coherent modules to the
chapter on derived categories of schemes

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.

Fix notation

	Try to make notation concerning quasi-coherent and adequate
	modules more consistent.

Cohomology of unbounded complexes

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

Whitespace changes

LaTeX: \Sch

	Introduced a new macro

	\def\Sch{\textit{Sch}}

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

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.

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.