Low-codimensional associated primes of graded components of local cohomology modules

Abstract

Let R = ⊕n≥0 Rn be a homogeneous noetherian ring and let M be a finitely generated graded R-module. Let HR+i (M) denote the ith local cohomology module of M with respect to the irrelevant ideal R+ := ⊕ n>0Rn of R. We show that if R0 is a domain, there is some s ∈ R0{0} such that the (R0)s-modules HR+i (M s are torsion-free (or vanishing) for all i. On use of this, we can deduce the following results on the asymptotic behaviour of the nth graded component HR+i (M)n of HR+i (M) for n → ∞: if R0 is a domain or essentially of finite type Show more