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October 2019 On a rigidity of some modular Galois deformations
Yuichi Shimada
Kodai Math. J. 42(3): 526-565 (October 2019). DOI: 10.2996/kmj/1572487231

Abstract

Let $F$ be a totally real field and $\mathbf{\rho} = (\rho_{\lambda})_{\lambda}$ be a compatible system of two dimensional $\lambda$-adic representations of the Galois group of $F$. We assume that $\mathbf{\rho}$ has a residually modular $\lambda$-adic realization for some $\lambda$. In this paper, we consider local behaviors of modular deformations of $\lambda$-adic realizations of $\mathbf{\rho}$ at unramified primes. In order to control local deformations at specified unramified primes, we construct certain Hecke modules. Applying Kisin's Taylor-Wiles system, we obtain an $R = T$ type result supplemented with local conditions at specified unramified primes. As a consequence, we shall show a potential rigidity of some modular deformations of infinitely many $\lambda$-adic realizations of $\mathbf{\rho}$.

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Yuichi Shimada. "On a rigidity of some modular Galois deformations." Kodai Math. J. 42 (3) 526 - 565, October 2019. https://doi.org/10.2996/kmj/1572487231

Information

Published: October 2019
First available in Project Euclid: 31 October 2019

zbMATH: 07174414
MathSciNet: MR4025757
Digital Object Identifier: 10.2996/kmj/1572487231

Rights: Copyright © 2019 Tokyo Institute of Technology, Department of Mathematics

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Vol.42 • No. 3 • October 2019
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