Associated primes and cofiniteness of local cohomology modules

Let a be an ideal of Noetherian ring R and let s be a non-negative integer. Let M be an R-module such that Ext(R)(s) (R/a, M) is finite R-module. If s is the first integer such that the local cohomology module H(a)(s) (M) is non a-cofinite, then we show that HOM(R) (R/a, H(a)(s) (M)) is finite. In particular, the set of associated primes of H(a)(s) (M) is finite. Let (R, m) 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 H(a)(n) (M) is not m-cofinite and show that n just depends on the support of M.