Counting the number of non-isomorphic top generalized local cohomology modules

Resumen

Let (R, m) be a commutative Noetherian local ring, a be a proper ideal of R and M and N be two finitely generated R-modules. In this paper, we give some results in order to count the number of non-isomorphic top generalized local cohomology modules, namely H_a^{d+n}(M,N), where dim N = n < \infty and pdim M = d < \infty. We prove that this number is equal to 2^{|Att_R(H_{m}^{d+n}(M,N))|}, when dim R=d+n and R is Cohen-Macaulay and complete with respect to the m-adic topology.