Generalized local cohomology and regularity of Ext modules

JOURNAL OF ALGEBRA

卷:319

Article

Chardin, Marc¹  Divaani-Aazar, Kamran² 

[1] Inst Math Jussieu, CNRS, F-75013 Paris, France

[2] Az Zahra Univ, Dept Math, Tehran 19834, Iran

关键词: generalized local cohomology;    regularity;   

DOI  :  10.1016/j.jalgebra.2007.11.032

来源: Elsevier

【 摘 要 】

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. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free