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| Paper IPM / M / 16419 |
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Let (R,\fm,k) be a local ring. We establish a totally reflexive analogue of the New
Intersection Theorem, provided for every totally reflexive R-module M, there is a big Cohen-Macaulay
R-module BM such that the socle of BM⊗RM is zero. When R is a quasi-specialization of a
\G-regular local ring or when M has complete intersection dimension zero, we show the existence of such
a big Cohen-Macaulay R-module. It is conjectured that if R admits a non-zero Cohen-Macaulay module of
finite Gorenstein dimension, then it is Cohen-Macaulay. We prove this conjecture if either R is a
quasi-specialization of a \G-regular local ring or a quasi-Buchsbaum local ring.
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