Witt vectors and $δ$-Cartier rings
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914019708764160 |
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| author | Magidson, Kirill |
| author_facet | Magidson, Kirill |
| contents | We give a universal property of the construction of the ring of $p$-typical Witt vectors of a commutative ring, endowed with Witt vectors Frobenius and Verschiebung, and generalize this construction to the derived setting. We define an $\infty$-category of $p$-typical derived $δ$-Cartier rings and show that the derived ring of $p$-typical Witt vectors of a derived ring is naturally an object in this $\infty$-category. Moreover, we show that for any prime $p$, the formation of the derived ring of $p$-typical Witt vectors gives an equivalence between the $\infty$-category of all derived rings and the full subcategory of all derived $p$-typical $δ$-Cartier rings consisting of $V$-complete objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03877 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Witt vectors and $δ$-Cartier rings Magidson, Kirill K-Theory and Homology Algebraic Geometry We give a universal property of the construction of the ring of $p$-typical Witt vectors of a commutative ring, endowed with Witt vectors Frobenius and Verschiebung, and generalize this construction to the derived setting. We define an $\infty$-category of $p$-typical derived $δ$-Cartier rings and show that the derived ring of $p$-typical Witt vectors of a derived ring is naturally an object in this $\infty$-category. Moreover, we show that for any prime $p$, the formation of the derived ring of $p$-typical Witt vectors gives an equivalence between the $\infty$-category of all derived rings and the full subcategory of all derived $p$-typical $δ$-Cartier rings consisting of $V$-complete objects. |
| title | Witt vectors and $δ$-Cartier rings |
| topic | K-Theory and Homology Algebraic Geometry |
| url | https://arxiv.org/abs/2409.03877 |