Characterizing Gorenstein rings using contracting endomorphisms

TL;DR

This paper characterizes Gorenstein rings through the vanishing of derived functors involving modules affected by contracting endomorphisms, extending classical results related to Frobenius and other endomorphisms.

Contribution

It provides new characterizations of Gorenstein rings using contracting endomorphisms, broadening the understanding beyond Frobenius-based results.

Findings

Characterizations of Gorenstein rings via derived functor vanishings

Extension of Kunz's results to general contracting endomorphisms

Analogues of classical theorems for broader classes of endomorphisms

Abstract

We prove several characterizations of Gorenstein rings in terms of vanishings of derived functors of certain modules or complexes whose scalars are restricted via contracting endomorphisms. These results can be viewed as analogues of results of Kunz (in the case of the Frobenius) and Avramov-Hochster-Iyengar-Yao (in the case of general contracting endomorphisms).