Gorenstein algebras and Hochschild cohomology

TL;DR

This paper characterizes when fiber rings are Gorenstein in terms of Hochschild cohomology modules for certain ring homomorphisms, linking algebraic properties with cohomological invariants.

Contribution

It provides a new characterization of Gorenstein fiber rings using Hochschild cohomology modules in the context of flat, finite type ring homomorphisms.

Findings

Fiber rings are Gorenstein iff certain Ext modules vanish or have specific properties.

Hochschild cohomology modules encode Gorenstein properties of fiber rings.

The characterization applies to flat, finite type homomorphisms over Gorenstein rings.

Abstract

For homomorphism K-->S of commutative rings, where K is Gorenstein and S is essentially of finite type and flat as a K-module, the property that all non-trivial fiber rings of K-->S are Gorenstein is characterized in terms of properties of the cohomology modules Ext_n^{S\otimes_KS}S{S\otimes_KS}.