Canonical Witt formal scheme extensions and p-torsion groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929450945347584 |
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| author | Bertapelle, Alessandra Mazzari, Nicola Saha, Arnab |
| author_facet | Bertapelle, Alessandra Mazzari, Nicola Saha, Arnab |
| contents | We study the $n$-th arithmetic jet space of the $p$-torsion subgroup attached to a smooth commutative formal group scheme. We show that the $n$-th jet space above fits in the middle of a canonical short exact sequence between a power of the formal scheme of Witt vectors of length $n$ and the $p$-torsion subgroup we started with. This result generalizes a result of Buium on roots of unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_10382 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Canonical Witt formal scheme extensions and p-torsion groups Bertapelle, Alessandra Mazzari, Nicola Saha, Arnab Number Theory Algebraic Geometry 13F35, 14L05, 14L15, 14B20, 14G20 We study the $n$-th arithmetic jet space of the $p$-torsion subgroup attached to a smooth commutative formal group scheme. We show that the $n$-th jet space above fits in the middle of a canonical short exact sequence between a power of the formal scheme of Witt vectors of length $n$ and the $p$-torsion subgroup we started with. This result generalizes a result of Buium on roots of unity. |
| title | Canonical Witt formal scheme extensions and p-torsion groups |
| topic | Number Theory Algebraic Geometry 13F35, 14L05, 14L15, 14B20, 14G20 |
| url | https://arxiv.org/abs/2207.10382 |