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Generalized local cohomology and regularity of Ext modules

Marc Chardin·Kamran Divaani-Aazar
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Abstract

Let R be a Noetherian standard graded ring, and M and N two finitely generated graded R-modules. We introduce reg_R (M,N) by using the notion of generalized local cohomology instead of local cohomology, in the definition of regularity. We prove that reg_R (M,N)is finite in several cases. In the case that the base ring is a field, we show that reg_R (M,N)=reg (N)-indeg (M). This formula, together with a graded version of duality for generalized local cohomology, gives a formula for the minimum of the initial degrees of some Ext modules(in the case R is Cohen-Macaulay), of which the three usual definitions of regularity are special cases. Bounds for regularity of certain Ext modules are obtained, using the same circle of ideas.

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Marc Chardin, Kamran Divaani-Aazar. 2007-06-19. Generalized local cohomology and regularity of Ext modules. https://arxiv.org/abs/math/0701509

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