2013/08/27 by Mohammad Reza Doustimehr, Doustimehr, Mohammad Reza, Reza Naghipour +1
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #math.AC #msc:13D45 #msc:13E05 #msc:14B15
paper · pdf · doi:10.48550/arxiv.1308.5945
8 pages
arxiv created 2013/08/27 · arxiv updated 2013/08/28
Let R be a commutative Noetherian ring and let n be a non-negative integer. In this article, by using the theory of Gorenstein dimensions, it is shown that whenever R is a homomorphic image of a Noetherian Gorenstein ring, then the invariants inf\i∈\nat0| dim\Supp(\fbtH\fai(M))≥ nfor all t∈\nat0\ and inf\λ_\fa R\p^\fb R\p(M\p)| \p∈ \rm Spec R and dim R/ \p≥ n\ are equal, for every finitely generated R-module M and for every ideals \frak a, \frak b of R with \frak b⊆ \frak a. This generalizes the Faltings' Annihilator Theorem [G. Faltings, \it Über die Annulatoren lokaler Kohomologiegruppen, Arch. Math. \bf30 (1978) 473-476].