The Stacks project

fix small typos

Fix messed up proof in groupoids

Somehow didn't notice the arrow didn't go the way it was supposed to!

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.

Tags: Added new tags

Groupoids and simplicial schemes

	Write out the relationship between groupoids in schemes and
	simplicial schemes. Define quasi-coherent modules on simplicial
	schemes. Define cartesian ones. Work out what they are and prove
	elementary properties. Relate these to quasi-coherent modules on
	groupoid schemes. Use this to prove that a quasi-coherent module
	on a qc+qs+Noetherian groupoid is a filtered colimit of its
	coherent submodules.

	Also added: The usual argument in case the groupoid is affine
	and there is a basis for O(R) over O(U). However, as far as I
	can see this only gives that every module is a filtered colimit
	of finitely generated things. In other words, I don't know how
	to show that you can get finitely presented modules... Do you?