LOCALLY ANALYTIC VECTORS AND OVERCONVERGENT (phi, tau)-MODULES

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http://hdl.handle.net/10138/338254

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Gao , H & Poyeton , L 2021 , ' LOCALLY ANALYTIC VECTORS AND OVERCONVERGENT (phi, tau)-MODULES ' , Journal of the Institute of Mathematics of Jussieu , vol. 20 , no. 1 , 1474748019000148 , pp. 137-185 . https://doi.org/10.1017/S1474748019000148

Title: LOCALLY ANALYTIC VECTORS AND OVERCONVERGENT (phi, tau)-MODULES
Author: Gao, Hui; Poyeton, Leo
Contributor organization: Department of Mathematics and Statistics
Date: 2021-01
Language: eng
Number of pages: 49
Belongs to series: Journal of the Institute of Mathematics of Jussieu
ISSN: 1474-7480
DOI: https://doi.org/10.1017/S1474748019000148
URI: http://hdl.handle.net/10138/338254
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 pi be a fixed uniformizer of K, let K-infinity be the extension by adjoining to K a system of compatible p(n) th roots of pi for all n, and let L be the Galois closure of K-infinity. Using these field extensions, Caruso constructs the (phi, tau)-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 (phi, Gamma)-modules, we can establish the overconvergence property of the (phi, tau)-modules.
Subject: locally analytic vectors
overconvergence
(phi, tau)-modules
UNITARY PRINCIPAL SERIES
P-ADIC REPRESENTATION
NORM FIELD
EXTENSIONS
111 Mathematics
Peer reviewed: Yes
Rights: cc_by_nc_nd
Usage restriction: openAccess
Self-archived version: acceptedVersion


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