Associated primes of graded components of local cohomology modules

Abstract

The i-th local cohomology module of a finitely generated graded module M over a standard positively graded commutative Noetherian ring R, with respect to the irrelevant ideal R+ , is itself graded; all its graded components are finitely generated modules over R0 , the component of R of degree 0. It is known that the n-th component Hi R+ (M )n of this local cohomology module Hi R+ (M ) is zero for all n >> 0. This paper is concerned with the asymptotic behaviour of AssR 0 (Hi R+ (M )n ) as n → −∞. The smallest i for which such study is Show more