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History of tag 07YU

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changed the proof 2013-03-27 ba00249
New macro: \NL for naive cotangent complex

The naive cotangent complex is an important ingredient to several
topics discussed in the Stacks project. It deserves its own macro.
changed the statement 2013-03-27 c0b15e3
Excise finite type conditions

We need to have the functors T_x and Inf_x for all modules not just
for finite type ones. This actually simplifies the discussion a
tiny bit as we don't have to carry along the finite type conditions
everywhere.

Thanks to David Rydh for pointing this out (see
commit 2ccbbe3087e4dc2b1df2193c81ede7486931424c for more
information).
assigned tag 07YU 2012-07-03 3fe4cf9
Tags: Added new tags
changed the proof 2012-07-03 65e41c9
Sharpen criterion openness versality

	Just having a single map with two properties is enough...
created statement with label lemma-naive-obstruction-theory-gives-openness in artin.tex 2012-06-28 d82e033
Some material about obstruction theories

	This includes the notion of a naive obstruction theory and a
	proof that such a thing is good enough to give openness of
	versality. This was introduced on the blog

	http://math.columbia.edu/~dejong/wordpress/?p=2472

	It is just working out what you would get if you actually had an
	algebraic stack. It seems likely that Artin was motivated in
	formulating his axioms by the idea that such a thing should
	exist.

	Hopefully we can use this to prove openness of versality for
	some nice cases such as families of proper flat algebraic
	spaces... We'll see.