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Bibliographic Details
Main Authors: Poyeton, Léo, Vanni, Pietro
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2502.12341
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Table of Contents:
  • In this paper we explain how to attach to a family of $p$-adic representations of a product of Galois groups an overconvergent family of multivariable $(φ,Γ)$-modules, generalizing results from Pal-Zabradi and Carter-Kedlaya-Zabradi, using Colmez-Sen-Tate descent. We also define rings of multivariable crystalline and semistable periods, and explain how to recover this multivariable $p$-adic theory attached to a family of representations from its multivariable $(φ,Γ)$-module. We also explain how our framework allows us to recover the main results of Brinon-Chiarellotto-Mazzari on multivariable $p$-adic Galois representations.