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Paper   IPM / M / 8031
School of Mathematics
  Title:   On the annihilation of local cohomology modules
1.  J. Asadollahi
2.  Sh. Salarian
  Status:   Published
  Journal: J. Math. Kyoto Univ.
  Vol.:  46
  Year:  2006
  Pages:   357-365
  Supported by:  IPM
Let R be a (not necessary finite dimensional) commutative Noetherian ring and C be a semi-dualizing module over R. As a refinement of Auslander G-dimension, it is possible to define for any finitely-generated R-module M a G-dimension with respect to C, namely GC-dimension of M, that shares the nice properties of Auslander G-dimension. In this paper, we establish the Faltings' Annihilator Theorem and its uniform version (in the sense of Raghavan) for Local Cohomology modules, over the class of finitely generated R-modules of finite GC-dimension, provided R is Cohen-Macaulay. Our approach offers a generalized and unified treatment of all of the notions and techniques studied and applied already for the proof of Annihilator Theorem.

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