The Stacks project

LaTeX: \Ob

	Introduced a macro

	\def\Ob{\mathop{\rm Ob}\nolimits}

	and replaced any occurence of \text{Ob}( with \Ob(. There are
	still some occurences of \text{Ob} but these are sets, not the
	operator that takes the set of objects of a category.

LaTeX: \Sch

	Introduced a new macro

	\def\Sch{\textit{Sch}}

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

Begin translating etale to \'etale or \acute{e}tale (in Math mode).

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.