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arXiv · 2507.13988

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

Daniel McCormick
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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.

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Daniel McCormick. 2025-07-18. A Ghost Lemma for Commutative Ring Homomorphisms via Andr\'{e}-Quillen Homology. https://arxiv.org/abs/2507.13988

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