The Stacks project

Minor improvement + fix typos in descent

THanks to ZL
https://stacks.math.columbia.edu/tag/06VE#comment-8505
https://stacks.math.columbia.edu/tag/06VE#comment-8506

Yet another characterization of QCoh

Better handling QCoh in different topologies

Feels like doing penance for my sins!

Unfortunate error in descent

Medium bad I would say. Argh!

Trivialities on Picard functor

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

Whitespace changes

Whitespace changes

LaTeX: Remove useless brackets

LaTeX: \Sch

	Introduced a new macro

	\def\Sch{\textit{Sch}}

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

LaTeX: Hom and SheafHom

	Introduced the macros

	\def\Hom{\mathop{\rm Hom}\nolimits}
	\def\SheafHom{\mathop{\mathcal{H}\!{\it om}}\nolimits}

	and replaced all the occurences of \text{Hom} and \textit{Hom}
	with these.

LaTeX: \Spec

	Introduced the macro

	\def\Spec{\mathop{\rm Spec}}

	and changed all the occurences of \text{Spec} into \Spec.

Temporary fix for section on derived cats of adequate modules

	More to come soon.

Tags: Added new tags

	Also fixed a couple of references

Adequate modules

	This material is a bit speculative. The idea is to find the
	smallest abelian subcategory of all sheaves of modules on a big
	site which contains the quasi-coherent ones. We succeed in doing
	this and characterizing these sheaves. However, there are some
	further issues with this category, one of them being that it
	isn't closed under tensor product...

Quasi-coherent sheaves

	A little bit more. Next up: Presentations and quasi-coherent
	sheaves.