The Stacks project

Typos pointed out by Anfang Zhou

http://stacks.math.columbia.edu/tag/05NE#comment-779
http://stacks.math.columbia.edu/tag/05NH#comment-780
http://stacks.math.columbia.edu/tag/00HL#comment-782
http://stacks.math.columbia.edu/tag/01ED#comment-783
http://stacks.math.columbia.edu/tag/01UP#comment-789

LaTeX

Introduced a macro

\def\Ker{\text{Ker}}

and replace all occurrences of \text{Ker} with \Ker

More generalities about \Omega_{X/S}

Clean up treatment module of differentials

Move the construction of \Omega to the setting of ringed spaces.
Redefine the module of differentials using the universal property. The
agreement with the conormal sheaf of the diagonal is now a lemma. Tried
to find all places where this was used...

Clean up treatment module of differentials

Move the construction of \Omega to the setting of ringed spaces.
Redefine the module of differentials using the universal property. The
agreement with the conormal sheaf of the diagonal is now a lemma. Tried
to find all places where this was used...

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...

More Morphisms Spaces: Module of differentials

	Started to write about module of differentials of a morphism of
	algebraic spaces. We want to use it in the discussion of
	formally smooth morphisms.

	This required some preliminary work improving the exposition in
	a few other plaves.

Started tags infrastructure

	new file:   scripts/add_tags.py
	modified:   scripts/functions.py
	new file:   tags/initial_tags
	new file:   tags/tags

Finished with differentials for now and rudimentary version of section
on smooth morphisms

	modified:   morphisms.tex