Locally analytic vectors and overconvergent (φ, τ)-modules

2018/04/22 by Hui Gao, Gao, Hui, Léo Poyeton +1
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.1804.08106

Abstract

Let p be a prime, let K be a complete discrete valuation field of characteristic 0 with a perfect residue field of characteristic p, and let G_K be the Galois group. Let π be a fixed uniformizer of K, let K_∞ be the extension by adjoining to K a system of compatible pⁿ-th roots of π for all n, and let L be the Galois closure of K_∞. Using these field extensions, Caruso constructs the (φ, τ)-modules, which classify p-adic Galois representations of G_K. In this paper, we study locally analytic vectors in some period rings with respect to the p-adic Lie group Gal(L/K), in the spirit of the work by Berger and Colmez. Using these locally analytic vectors, and using the classical overconvergent (φ, Γ)-modules, we can establish the overconvergence property of the (φ, τ)-modules.

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