Associated primes and cofiniteness of local cohomology modules

Abstract

Let Open image in new window be an ideal of Noetherian ring R and let s be a non-negative integer. Let M be an R-module such that Open image in new window is finite R-module. If s is the first integer such that the local cohomology module Open image in new window is non Open image in new window-cofinite, then we show that Open image in new window is finite. In particular, the set of associated primes of Open image in new windowis finite. Let Open image in new window be a local Noetherian ring and let M be a finite R-module. We study the last integer n such that the local cohomology module Open image in new window is not Open image in new window-cofinite and show that n just depends on the support of M.