History of tag 07YP
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changed the statement
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2017-04-11 |
04fef69 |
New macro: \Ext
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changed the statement
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2013-12-22 |
e179438 |
LaTeX
Introduced a macro
\def\Ker{\text{Ker}}
and replace all occurrences of \text{Ker} with \Ker
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changed the statement
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2013-06-04 |
80afd57 |
\text{Hom} ---> \Hom
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changed the statement
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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.
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changed the statement
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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).
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changed the statement
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2013-03-27 |
2ccbbe3 |
Fix error in artin.tex pointed out by David Rydh
The proof of Lemma Tag 07YM was wrong in two ways:
-- We were using the condition (RS*) in some cases where it didn't
apply, namely for an extension A' of a Noetherian ring A by a
module isomorphic to the residue field of a finite type point.
-- The second mistake was in some sense the same mistake thinking that
the ring A' was Noetherian.
The solution, as pointed out by David Rydh, is twofold:
-- Strengthen assumption (RS*) to cover the first snafu
-- Only prove openess of versality at closed points
As far as I can see, this is harmless in all applications.
There are still some things left to fix. In particular, some of
the material concerning T_x(-) has to be fixed to deal with
non-finitely generated modules.
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assigned tag 07YP
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2012-07-03 |
3fe4cf9
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Tags: Added new tags
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created statement with label definition-naive-obstruction-theory in artin.tex
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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.
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