Characterising properties of commutative rings using Witt vectors
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917968373350400 |
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| author | Muñoz--Bertrand, Rubén |
| author_facet | Muñoz--Bertrand, Rubén |
| contents | We give equivalences between given properties of a commutative ring, and other properties on its ring of Witt vectors. Amongst them, we characterise all commutative rings whose rings of Witt vectors are Noetherian. We define a new category of commutative rings called preduced rings, and explain how it is the category of rings whose ring of Witt vectors has no $p$-torsion. We then extend this characterisation to the torsion of the de Rham-Witt complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20115 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterising properties of commutative rings using Witt vectors Muñoz--Bertrand, Rubén Commutative Algebra Algebraic Geometry Number Theory We give equivalences between given properties of a commutative ring, and other properties on its ring of Witt vectors. Amongst them, we characterise all commutative rings whose rings of Witt vectors are Noetherian. We define a new category of commutative rings called preduced rings, and explain how it is the category of rings whose ring of Witt vectors has no $p$-torsion. We then extend this characterisation to the torsion of the de Rham-Witt complex. |
| title | Characterising properties of commutative rings using Witt vectors |
| topic | Commutative Algebra Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2503.20115 |