Algebraic monodromy groups of l-adic representations of Gal(ℚ∕ℚ)

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 $Gal (\bar{ℚ} ∕ ℚ)$ 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.

Keywords

Galois representation, Galois deformation theory

Mathematical Subject Classification 2010

Primary: 11F80

Milestones

Received: 15 June 2018

Revised: 18 October 2018

Accepted: 20 November 2018

Published: 18 August 2019

Authors

Shiang Tang
Department of Mathematics University of Utah Salt Lake City, UT United States

Vol. 13, No. 6, 2019

Shiang Tang

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors