Asymptotic behaviour of cohomology: tameness, supports and associated primes

Abstract

Abstract. Let R = ⊕ n≥0 R n be a homogeneous Noetherian ring, let X = Proj(R) and let F be a coherent sheaf of O X -modules. We present a few results about the behaviour of the finitely generated R 0 -modules H

Results on Graded Generalized Local Cohomology

“…Furthermore, it was proved in Zamani (2006, Corollary 3.6) that we also have tameness property in the top level i = pd M + dim N/ 0 N . In the next theorem, we shall prove another tameness result which improves this earlier result (see also Brodmann, 2005). For this, we shall have to use the following results.…”

A natural map in local cohomology

“…In order to refine and complete [6, Theorem 4.4] we study the asymptotic behavior of the kernel and cokernel of the natural graded homomorphism between the graded modules Ext s R (R/R + , M) and Hom R (R/R + , H s R+ (M )). For more information on the notions in (a), (b) and (c), see [3].…”

On the asymptotic behaviour of associated primes of generalized local cohomology modules

“…It is well known that Hj{N) is equipped with a natural grading for all i 6 N o (compare [8,Remarks 12.3.6]). The associated primes of graded components of local cohomology modules were studied in a number of papers (compare [3][4][5][6][7]12,13,17,18]). Brodmann and Hellus, in [6], showed that if k is an integer such that H' R+ (N) is finitely generated for all i < k, then the associated prime ideals of H R+ (N) n is asymptotically stable as n -> -oo.…”