Local cohomology modules via certain flat extension rings

Let (R,m) be a Noetherian local ring and M a finitely generated R-module. Let P∈Spec(Rˆ) and p=P∩R. Then the natural map Rp→RˆP is a flat local homomorphism. In this paper, we provide some relations between the two sets of attached primes of the Artinian local cohomology modules HPRˆPi+rP(Mp⊗RpRˆP) and HpRpi(Mp), where i≥0 is an integer and rP=dim⁡(RˆP/pRˆP). Then, we compute the dimension and multiplicity of HPRˆPi+rP(Mp⊗RpRˆP) in terms of that of HpRpi(Mp) respectively. As applications, we give connections between the Cohen-Macaulayness in dimension >s of MˆP and that of Mp, for an integer s≥−1.