The Stacks project

Lemma on classifying stack of a group alg space

LaTeX: \etale

Introduced the macro

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

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

End conversion of etale to \'etale.

More on quotient stacks

	Followup on commit 6bbac683b9434c98c2ba3a73dc269a8f0116cc2b

Tags: Added new tags

The stack of torsors

	There are many different possible definitions for the stack of
	torsors for a group algebraic space G over a base B. You can
	look at principal homogeneous spaces for the fpqc topology, or,
	and this is more natural for us, look at fppf G-torsors. One
	reason this is natural is that you get the same thing as looking
	at G-torsors where you think of G as a sheaf!

	If G is a group scheme over a scheme, then you could also just
	look at those fppf G-torsors which are representable. Of course
	this is somehow completely the wrong thing to do, but on the
	other hand it is what comes natural since we know more about
	schemes than about algebraic spaces.

	We try to discuss all the possible variants extensively in a
	section in the chapter "Examples of Stacks". In the future we
	will add some lemmas/propositions/theorems saying that if G has
	reasonable properties then these stacks all agree.