Bloch-Kato groups over perfectoid fields and Galois theory of $p$-adic periods

Gautier Ponsinet

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arXiv · 2412.00227

Bloch-Kato groups over perfectoid fields and Galois theory of $p$-adic periods

Gautier Ponsinet

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Abstract

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.

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BibTeX RIS

Gautier Ponsinet. 2024-11-29. Bloch-Kato groups over perfectoid fields and Galois theory of $p$-adic periods. https://arxiv.org/abs/2412.00227

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