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| Paper IPM / M / 8031 |
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| Abstract: | |||||
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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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