A Ghost Lemma for Commutative Ring Homomorphisms via Andr\'{e}-Quillen Homology

TL;DR

This paper extends ghost map theory to commutative rings using Andre9-Quillen homology, providing new generalizations of Kunz's theorem and results for complete intersection rings.

Contribution

It introduces a ghost lemma for commutative rings via Andre9-Quillen homology, broadening the application of ghost maps beyond derived categories.

Findings

Derived category ghost maps adapted to rings.

A characteristic-independent generalization of Kunz's theorem.

An analogue result for complete intersection rings.

Abstract

We adapt the theory of ghost maps from derived categories to the setting of commutative rings using Andr\'{e}-Quillen homology. The Frobenius endomorphism is a primary example of a ghost map in this setting. We prove an analogue of the ghost lemma for rings and demonstrate its utility by deducing a characteristic independent generalization of Kunz's theorem and an analogue for complete intersection rings.