Formalization in Lean of faithfully flat descent of projectivity
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914368795443200 |
|---|---|
| author | Shaul, Liran |
| author_facet | Shaul, Liran |
| contents | We formalize in Lean the following foundational result in commutative algebra: Let $R \to S$ be a faithfully flat map of (not necessarily noetherian) commutative rings, and let $P$ be an arbitrary $R$-module. Then $P$ is projective over $R$ if and only if $S\otimes_R P$ is projective over $S$. This formalizes and verifies Perry's fix of a subtle gap in the classical work of Raynaud and Gruson, a result which is a key ingredient in the study of finitistic dimension of commutative noetherian rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04376 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Formalization in Lean of faithfully flat descent of projectivity Shaul, Liran Commutative Algebra Rings and Algebras Primary: 13C10, 16D40, 68V20 We formalize in Lean the following foundational result in commutative algebra: Let $R \to S$ be a faithfully flat map of (not necessarily noetherian) commutative rings, and let $P$ be an arbitrary $R$-module. Then $P$ is projective over $R$ if and only if $S\otimes_R P$ is projective over $S$. This formalizes and verifies Perry's fix of a subtle gap in the classical work of Raynaud and Gruson, a result which is a key ingredient in the study of finitistic dimension of commutative noetherian rings. |
| title | Formalization in Lean of faithfully flat descent of projectivity |
| topic | Commutative Algebra Rings and Algebras Primary: 13C10, 16D40, 68V20 |
| url | https://arxiv.org/abs/2603.04376 |