Let $(R,m,k)$ be a (noetherian) regular local ring of depth=dimension $d$, and let $D$ be a dualizing module for $R$ (say, the injective envelope of $R/m$).
Then is $D_p$ dualizing for $R_p$ for any prime $p$ of $R$ (more generally, if $R$ is Gorenstein and $p$ is a prime such that $R_p$ is also Gorenstein)? If it is true, could I have a reference for a proof?
Bump!