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

2024/11/29 by Gautier Ponsinet, Ponsinet, Gautier
Mathematics · #Algebraic Geometry and Number Theory #advanced mathematical theories #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2412.00227

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 B_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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