Bloch-Kato groups over perfectoid fields and Galois theory of $p$-adic periods
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909410260942848 |
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| author | Ponsinet, Gautier |
| author_facet | Ponsinet, Gautier |
| contents | We relate the structure of the Bloch-Kato groups associated with a de Rham Galois representation over a perfectoid field to the Galois theory of the ring $\mathbf{B}_\mathrm{dR}^+$ of $p$-adic periods. As an application, we answer the question raised by Coates and Greenberg and motivated by Iwasawa theory to compute the Bloch-Kato groups over perfectoid fields in new cases, generalising results of Coates and Greenberg and the author. Our method relies on the classification of vector bundles over the Fargues-Fontaine curve. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_00227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bloch-Kato groups over perfectoid fields and Galois theory of $p$-adic periods Ponsinet, Gautier Number Theory 11R23, 14G45 We relate the structure of the Bloch-Kato groups associated with a de Rham Galois representation over a perfectoid field to the Galois theory of the ring $\mathbf{B}_\mathrm{dR}^+$ of $p$-adic periods. As an application, we answer the question raised by Coates and Greenberg and motivated by Iwasawa theory to compute the Bloch-Kato groups over perfectoid fields in new cases, generalising results of Coates and Greenberg and the author. Our method relies on the classification of vector bundles over the Fargues-Fontaine curve. |
| title | Bloch-Kato groups over perfectoid fields and Galois theory of $p$-adic periods |
| topic | Number Theory 11R23, 14G45 |
| url | https://arxiv.org/abs/2412.00227 |