A Ghost Lemma for Commutative Ring Homomorphisms via André-Quillen Homology
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913948728557568 |
|---|---|
| author | McCormick, Daniel |
| author_facet | McCormick, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Ghost Lemma for Commutative Ring Homomorphisms via André-Quillen Homology McCormick, Daniel Commutative Algebra 13D03 (primary), 13D05, 13D09, 13H05, 13H10 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. |
| title | A Ghost Lemma for Commutative Ring Homomorphisms via André-Quillen Homology |
| topic | Commutative Algebra 13D03 (primary), 13D05, 13D09, 13H05, 13H10 |
| url | https://arxiv.org/abs/2507.13988 |