Residual irreducibility of compatible systems

Author: 

Patrikis, S
Snowden, A
Wiles, A

Publication Date: 

24 December 2016

Journal: 

International Mathematics Research Notices

Last Updated: 

2020-02-01T10:03:25.017+00:00

Issue: 

2

Volume: 

2018

DOI: 

10.1093/imrn/rnw241

page: 

571-587

abstract: 

We show that if {pl} is a compatible system of absolutely irreducible Galois representations of a number field then the residual representation p is absolutely irreducible for l in a density 1 set of primes. The key technical result is the following theorem: the image of pl is an open subgroup of a hyperspecial maximal compact subgroup of its Zariski closure with bounded index (as l varies). This result combines a theorem of Larsen on the semi-simple part of the image with an analogous result for the central torus that was recently proved by Barnet-Lamb, Gee, Geraghty, and Taylor, and for which we give a new proof.

Symplectic id: 

665998

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article