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History of tag 07Y9

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changed the proof 2024-06-17 0930990
fix small typos
changed the statement 2017-04-24 a5929e7
Generalize section on infinitesimal deformations

We want to use the definitions even when the base scheme is not
necessarily Noetherian.

We also removed the requirement in (RS*) that the affine schemes in
question map into an affine open of the base scheme. This is never
needed when one actually verifies a given stack has (RS*) and in
fact this more general notion is always a consequence of the
original restricted one.
changed the proof 2016-11-26 b4909aa
Check agreement infinitesimal deformation spaces
changed the statement 2013-12-22 e179438
LaTeX

Introduced a macro

\def\Ker{\text{Ker}}

and replace all occurrences of \text{Ker} with \Ker
changed the statement and the proof 2013-06-04 507df54
\text{Mod}(R) ---> \text{Mod}_R and similar
changed the statement and the proof 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 07Y9 2012-07-03 3fe4cf9
Tags: Added new tags
created statement with label lemma-properties-lift-RS-star 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.