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The Stacks project

History of tag 07YN

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changed the statement 2017-04-11 04fef69
New macro: \Ext
changed the statement and 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 and the proof 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.
assigned tag 07YN 2012-07-03 3fe4cf9
Tags: Added new tags
created statement with label lemma-openness in artin.tex 2012-07-03 65e41c9
Sharpen criterion openness versality

	Just having a single map with two properties is enough...