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Paper   IPM / M / 16419
School of Mathematics
  Title:   On the new intersection theorem for totally reflexive modules
  Author(s): 
1.  Kamran Divaani-Aazar
2.  Ehsan Tavanfar
3.  Masoud Tousi (Joint with F. Mohammadi Aghjeh Mashhad)
  Status:   Published
  Journal: Collect. Math.
  Year:  2021
  Pages:   DOI: 10.1007/s13348-019-00264-3
  Supported by:  IPM
  Abstract:
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 BMRM 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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