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2019 Algebraic monodromy groups of $l$-adic representations of Gal$(\overline{\mathbb{Q}} /\mathbb{Q})$
Shiang Tang
Algebra Number Theory 13(6): 1353-1394 (2019). DOI: 10.2140/ant.2019.13.1353

Abstract

In this paper we prove that for any connected reductive algebraic group G and a large enough prime l , there are continuous homomorphisms

Gal ( ̄ ) G ( ̄ l )

with Zariski-dense image, in particular we produce the first such examples for SL n , Sp 2 n , Spin n , E 6 sc and E 7 sc . To do this, we start with a mod- l representation of Gal ( ̄ ) related to the Weyl group of G and use a variation of Stefan Patrikis’ generalization of a method of Ravi Ramakrishna to deform it to characteristic zero.

Citation

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Shiang Tang. "Algebraic monodromy groups of $l$-adic representations of Gal$(\overline{\mathbb{Q}} /\mathbb{Q})$." Algebra Number Theory 13 (6) 1353 - 1394, 2019. https://doi.org/10.2140/ant.2019.13.1353

Information

Received: 15 June 2018; Revised: 18 October 2018; Accepted: 20 November 2018; Published: 2019
First available in Project Euclid: 21 August 2019

MathSciNet: MR3994568
Digital Object Identifier: 10.2140/ant.2019.13.1353

Subjects:
Primary: 11F80

Keywords: Galois deformation theory , Galois representation

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 6 • 2019
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