A Bass equality for Gorenstein injective dimension of modules finite over homomorphisms

Abstract

Let $R\to S$ be a local ring homomorphism and $N$ a finitely generated $S$-module. We prove that if the Gorenstein injective dimension of $N$ over $R$ is finite, then it equals the depth of $R$.

Minor updates incl. additional citations. Final version, to appear in Arch. Math. (Basel); 8 pp