Generalized local cohomology and the Intersection Theorem

2004/02/19 by Mohammad T. Dibaei, Siamak Yassemi, Dibaei, Mohammad T. +1
Mathematics · Medicine · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Pain Mechanisms and Treatments #math.AC #msc:13D05 #msc:13D22 #msc:13D25 #msc:13D45

paper · pdf · doi:10.48550/arxiv.math/0402310

13 pages

arxiv created 2004/02/19 · arxiv updated 2009/12/01

Abstract

Let R be commutative Noetherian ring and let \fa be an ideal of R. For complexes X and Y of R--modules we investigate the invariant inf\mathbf RΓ_\fa(\mathbf R\Hom_R(X,Y)) in certain cases. It is shown that, for bounded complexes X and Y with finite homology, dim Y≤dim\mathbf R\Hom_R(X,Y)≤\pd X+dim(X⊗^{\mathbf L}_RY)+sup X which strengthen the Intersection Theorem. Here inf X and sup X denote the homological infimum, and supremum of the complex X, respectively.

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