A Ghost Lemma for Commutative Ring Homomorphisms via Andr\'{e}-Quillen Homology
Commutative Algebra
2025-07-21 v1
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.
Cite
@article{arxiv.2507.13988,
title = {A Ghost Lemma for Commutative Ring Homomorphisms via Andr\'{e}-Quillen Homology},
author = {Daniel McCormick},
journal= {arXiv preprint arXiv:2507.13988},
year = {2025}
}
Comments
19 pages