Symmetry theorems for Ext vanishing

Details Symmetry theorems for Ext vanishing Symmetry theorems for Ext vanishing

2004-08-10

arxiv.org/abs/math/0408127v2

Mathematics

Rings and Algebras

18 pages. Paper completely rewritten since version 1 contains an error in the proof of Proposition 2.3

Scientific paper

It was proved by Avramov and Buchweitz that if A is a commutative local complete intersection ring with finitely generated modules M and N, then the Ext groups between M and N vanish from some step if and only if the Ext groups between N and M vanish from some step. This paper shows that the same is true under the weaker conditions that A is Gorenstein and that M and N have finite complete intersection dimension. The result is also proved if A is Gorenstein and has finite Cohen-Macaulay type. Similar results are given for two types of non-commutative rings: Frobenius algebras and complete semi-local algebras.

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