On Gorenstein fiber products and applications

Abstract

We show that a non-trivial fiber product $S{\times }_{k}T$ of commutative noetherian local rings $S,T$ with a common residue field $k$ is Gorenstein if and only if it is a hypersurface of dimension 1. In this case, both $S$ and $T$ are regular rings of dimension 1. We also give some applications of this result.

This paper is subsumed by the new paper: arXiv:1802.00307

References in corpus (1)

• On the existence of non-free totally reflexive modules