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COMPATIBLE SYSTEMS OF GALOIS REPRESENTATIONS ASSOCIATED TO THE EXCEPTIONAL GROUP $E_{6}$

Part of: Discontinuous groups and automorphic forms Linear algebraic groups and related topics

Published online by Cambridge University Press:  06 February 2019

GEORGE BOXER ,
FRANK CALEGARI ,
MATTHEW EMERTON ,
BRANDON LEVIN ,
KEERTHI MADAPUSI PERA  and
STEFAN PATRIKIS
GEORGE BOXER
Affiliation:
Department of Mathematics, University of Chicago, 5734 S University Ave Chicago, IL 60637, USA; gboxer@math.uchicago.edu, fcale@math.uchicago.edu, emerton@math.uchicago.edu
FRANK CALEGARI
Affiliation:
Department of Mathematics, University of Chicago, 5734 S University Ave Chicago, IL 60637, USA; gboxer@math.uchicago.edu, fcale@math.uchicago.edu, emerton@math.uchicago.edu
MATTHEW EMERTON
Affiliation:
Department of Mathematics, University of Chicago, 5734 S University Ave Chicago, IL 60637, USA; gboxer@math.uchicago.edu, fcale@math.uchicago.edu, emerton@math.uchicago.edu
BRANDON LEVIN
Affiliation:
Department of Mathematics, University of Arizona, 617 N. Santa Rita Avenue, Tucson, Arizona 85721, USA; bwlevin@math.arizona.edu
KEERTHI MADAPUSI PERA
Affiliation:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467, USA; keerthi.madapusipera@bc.edu
STEFAN PATRIKIS
Affiliation:
Department of Mathematics, The University of Utah, 155 S 1400 E, Salt Lake City, UT 84112, USA; patrikis@math.utah.edu

Abstract

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We construct, over any CM field, compatible systems of $l$-adic Galois representations that appear in the cohomology of algebraic varieties and have (for all $l$) algebraic monodromy groups equal to the exceptional group of type $E_{6}$.

MSC classification

Primary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 11F80: Galois representations
Secondary: 20G41: Exceptional groups
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 7 , 2019 , e4
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2019

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