Finiteness of extension functors of local cohomology modules

Abstract

Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$ and $M$ a finitely generated $R$--module. Let $t$ be a non-negative integer such that $\H^i_\fa(M)$ is $\fa$--cofinite for all $i<t$. It is well--known that $\Hom_R(R/\fa,\H^t_\fa(M))$ is finitely generated $R$--module. In this paper we study the finiteness of $\Ext^1_R(R/\fa,\H^t_\fa(M))$ and $\Ext^2_R(R/\fa,\H^t_\fa(M))$.