A Ghost Lemma for Commutative Ring Homomorphisms via André-Quillen Homology

Abstract

We adapt the theory of ghost maps from derived categories to the setting of commutative rings using André-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.

19 pages