The Stacks project

Clarify stuff on deformations of maps thickenings

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...

End conversion of etale to \'etale.

More Morphisms: Edit

	Explain when it is neccesary to have affine test schemes and
	when it is unnecessary.

More on Morphisms: Actions by derivations

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

Tags: Added new tags

Infinitesimal deformations of maps: Algebraic space case

	This is really not the right way to do it, but it does seem to
	work.

Actions by derivations: Not done yet

	Some more results on acting by derivations on morphisms. The
	main point is to make everything sufficiently general so that we
	can use it in the setting of morphisms of algebraic spaces.

More on Morphisms: Etale localization and infinitesimal defos of maps