EXTENSION FUNCTORS OF LOCAL COHOMOLOGY MODULES AND SERRE CATEGORIES OF MODULES

Let (R, m) be a complete Noetherian local ring, I a proper ideal of R and M, N two finitely generated R-modules such that Supp(N) subset of V (I). Let t >= 0 be an integer such that for each 0 >= i >= t, the R-module H-i(I) (M) is in dimension < n. Then we show that each element L of the set J, which is defined as: [GRAPHICS] is finite. Also, as an immediately consequence of this result it follows that the R-modules Ext(j)(R) (N, HiI ( M)) are in dimension < n-1, for all integers i, j >= 0, whenever dim(M/IM) = n. These results generalizes the main results of Huneke-Koh [17], Delfino [10], Chiriacescu [9], Asadollahi-Naghipour [1], Quy [18], Brodmann-Lashgari [7], Bahmanpour-Naghipour [5] and Bahmanpour et al. [6] in the case of complete local rings.