Associated primes and cofiniteness of local cohomology modules

Paper

Abstract

Let

be an ideal of Noetherian ring

and let

be an

-module such that

is finite

-module for every

. If

is the first integer such that the local cohomology module

is non

-cofinite, then we show that

is finite. Specially, the set of associated primes of

is finite. Next assume

is a local Noetherian ring and

is a finitely generated module. We study the last integer

such that the local cohomology module

is not

-cofinite and show that

just depends on the support of