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1 November 2021 Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations
Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis
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Duke Math. J. 170(16): 3505-3599 (1 November 2021). DOI: 10.1215/00127094-2021-0003

Abstract

We study irreducible odd mod p Galois representations ρ¯:Gal(FF)G(Fp), for F a totally real number field and G a general reductive group. For pG,F0, we show that any ρ¯ that lifts locally, and at places above p to de Rham and Hodge–Tate regular representations, has a geometric p-adic lift. We also prove non-geometric lifting results without any oddness assumption.

Dedication

In memory of Jean-Pierre Wintenberger, 1954–2019

Citation

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Najmuddin Fakhruddin. Chandrashekhar Khare. Stefan Patrikis. "Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations." Duke Math. J. 170 (16) 3505 - 3599, 1 November 2021. https://doi.org/10.1215/00127094-2021-0003

Information

Received: 23 July 2019; Revised: 29 September 2020; Published: 1 November 2021
First available in Project Euclid: 18 October 2021

Digital Object Identifier: 10.1215/00127094-2021-0003

Subjects:
Primary: 11F80
Secondary: 11R34 , 11R39

Keywords: deformation theory of Galois representations , geometric Galois representations

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 16 • 1 November 2021
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