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A criterion for regularity of local rings

Abstract:

It is proved that a noetherian commutative local ring A containing a field is regular if there is a complex M of free A-modules with the following properties: Mi = 0 for i ∉ [ 0, dim A ]; the homology of M has finite length; H0 ( M ) contains the residue field of A as a direct summand. This result is an essential component in the proofs of the McKay correspondence in dimension 3 and of the statement that threefold flops induce equivalences of derived categories. To cite this article: T. Bridg...

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Publisher copy:
10.1016/j.crma.2006.03.019

Authors


Bridgeland, T More by this author
Iyengar, S More by this author
Journal:
Comptes Rendus Mathematique
Volume:
342
Issue:
10
Pages:
723-726
Publication date:
2006-05-15
DOI:
ISSN:
1631-073X
URN:
uuid:51d8eacf-fac1-4fbf-8fd3-4e95b1dd4c9a
Source identifiers:
284266
Local pid:
pubs:284266
Language:
English

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