The Stacks project

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).

Relative inertia fibred category

	We pay for not introducing relative inertia fibred categories by
	having to do it all over again.

Definition of a presentation of an algebraic stack

	Plus some small local improvements.

An algebraic stack with trivial inertia is an algebraic space

	As advertised on the blog.

Bootstrap: Added new chapter

	It seems better to discuss the bootstrap theorems in a separate
	chapter following the discussion of the basic material on
	algebraic spaces. This can then be used in the chapter on
	algebraic stacks when discussing presentations and what not.

	The goal is to prove the theorem that an fppf sheaf F for which
	there exists a scheme X and a morphism f : X --> F such that
		f is representable by algebraic spaces
		f is flat, surjective and locally of finite presentation
	is automatically an algebraic space. We have almost all the
	ingredients ready except for a slicing lemma -- namely somehow
	lemma 3.3 part (1) of Keel-Mori.

Tags: added new tags

Algebraic stacks: Deligne-Mumford with trivial inertia is a space

	To prove this for a general algebraic stack we will first prove
	a characterization of a DM stack as an algebraic stack whose
	inertia is formally unramified, or equivalently diagonal is
	formally unramified. Before we do this it makes sense to change
	the notion of unramified as suggested by David Rydh (see
	documentation/todo-list).

	We also added the proof of the statement that the property of
	being an algebraic stack is invariant under equivalences.