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The Stacks project

History of tag 07YZ

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type time link
changed the proof 2017-04-11 04fef69
New macro: \Ext
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 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.
changed the proof 2013-01-02 d0096b5
Small changes
assigned tag 07YZ 2012-07-03 3fe4cf9
Tags: Added new tags
created statement with label lemma-dual-openness in artin.tex 2012-07-03 1e43491
Application to openness of versality

	Exactly as predicted.