The Stacks project

Coherent on schemes vs on algebraic spaces

Thanks for a comment by Anonymous
https://stacks.math.columbia.edu/tag/07UC#comment-7867

Better handling QCoh in different topologies

Feels like doing penance for my sins!

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.

Unify notation \textit{QCoh}

LaTeX: \etale

Introduced the macro

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

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

Added a reference

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: uniformize notation

Quasi-coherent sheaves

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

Properties of (quasi-coherent) modules on an algebraic space

End conversion of etale to \'etale.

Relocalizing morphisms of (ringed) topoi

	There is quite a bit of duplication here, but it seems
	convenient to be able to talk about this both when given
	explicit sites defining the topoi and when you are just given an
	abstract morphism of (ringed) topoi.

Tags: Added new tags

	Also commented obsolete tags corresponding to sections of
	desirables.tex that have been removed.

Morphisms of Spaces: Quasi-coherence and pushforward

	This is surprisingly painful. We also put in some more general
	properties of quasi-coherent sheaves on ringed sites as well as
	algebraic spaces.