Associated primes and cofiniteness of local cohomology modules

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Let a be an ideal of Noetherian ring R and let M be an R-module such that Extⁱᵣ(R/a,M) is finite R-module for every i. If s is the first integer such that the local cohomology module Hˢₐ(M) is non a-cofinite, then we show that Homᵣ(R/a, Hˢₐ(M)) is finite. Specially, the set of associated primes of Hˢₐ(M) is finite. Next assume (R,m) is a local Noetherian ring and M is a finitely generated module. We study the last integer n such that the local cohomology module Hⁿₐ(M) is not m-cofinite and show that n just depends on the support of M.