The Stacks project

Fix typo

Thanks to Casimir Kothari
https://stacks.math.columbia.edu/tag/02HT#comment-8634

Change tensor product

Thanks to Brian Conrad
http://stacks.math.columbia.edu/tag/02HT#comment-1939

Typo in algebra.tex

Thanks to Matthew Emerton
http://stacks.math.columbia.edu/tag/02HT#comment-900

LaTeX

Introduced a macro

\def\Ker{\text{Ker}}

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

Cleanup section formally smooth ring maps

Fix use NL in algebra chapter

	Fallout from improvement in previous commit.

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...

Added dimension formula and relation to universally catenary rings
Added examples of
	Noetherian ring of infinite dimension
	Non catenary Noetherian local ring

	modified:   algebra.tex
	modified:   examples.tex
	modified:   my.bib

Added new tags

	modified:   algebra.tex
	modified:   tags/tags

Added new tags

	modified:   algebra.tex
	modified:   tags/tags

Lifting criterion smoothness using artinian rings

	modified:   algebra.tex
	modified:   more-morphisms.tex
	modified:   morphisms.tex

Start of lifting criterion smoothness using artinian rings

	modified:   algebra.tex
	modified:   more-morphisms.tex