On injective resolutions of local cohomology modules

Abstract

Let $K$ be a field of characteristic zero and let $R = K[X_1,\ldots,X_n]$. Let $I$ be an ideal in $R$ and let $M = H^i_I(R)$ be the $i^{th}$-local cohomology module of $R$ with respect to $I$. Let $c = \ injdim \ M$. We prove that if $P$ is a prime ideal in $R$ with Bass number $\mu_c(P,M) > 0$ then $P$ is a maximal ideal in $R$.