The Stacks project

Clarify stuff on deformations of maps thickenings

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.

Bunch of changes

	(1) Starting to write about thickenings of algebraic spaces
	(2) Change Omega^1_{X/S} to Omega_{X/S}
	(3) Introduced universal homeomorphisms for algebraic spaces
	(4) If X ---> Y is a surjective, integral morphism of schemes
	and X is an affine scheme, then Y is an affine scheme
	(4) Topological invariance of the site X_{spaces, etale} of an
	algebraic space X (proof unfinished}

	In order to see that also X_{etale} is a topological invariant
	we (I think) need to prove the following result: If X --> Y is a
	integral, universally injective, surjective morphism of
	algebraic spaces then X is a scheme if and only if Y is a
	scheme. There are two proofs of this result in the literature
	(one by David Rydh and one by Brian Conrad); both reduce the
	result to the Noetherian case by limit arguments. I would
	prefer a more direct argument...

Tags: added tags

More on Morphisms: Actions by derivations

	A bit of an improvement of the exposition in the section on
	deformations of maps and derivations.