Irreducibility of automorphic Galois representations of G L ( n ) , n at most 5

Frank Calegari[1]; Toby Gee[1]

  • [1] Northwestern University Department of Mathematics 2033 Sheridan Road Evanston IL 60208-2730 (USA)

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 5, page 1881-1912
  • ISSN: 0373-0956

Abstract

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Let π be a regular, algebraic, essentially self-dual cuspidal automorphic representation of GL n ( 𝔸 F ) , where F is a totally real field and n is at most 5 . We show that for all primes l , the l -adic Galois representations associated to π are irreducible, and for all but finitely many primes l , the mod l Galois representations associated to π are also irreducible. We also show that the Lie algebras of the Zariski closures of the l -adic representations are independent of l .

How to cite

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Calegari, Frank, and Gee, Toby. "Irreducibility of automorphic Galois representations of $GL(n)$, $n$ at most $5$." Annales de l’institut Fourier 63.5 (2013): 1881-1912. <http://eudml.org/doc/275430>.

@article{Calegari2013,
abstract = {Let $\pi $ be a regular, algebraic, essentially self-dual cuspidal automorphic representation of $\textrm\{GL\}_n(\{\mathbb\{A\}\}_F)$, where $F$ is a totally real field and $n$ is at most $5$. We show that for all primes $l$, the $l$-adic Galois representations associated to $\pi $ are irreducible, and for all but finitely many primes $l$, the mod $l$ Galois representations associated to $\pi $ are also irreducible. We also show that the Lie algebras of the Zariski closures of the $l$-adic representations are independent of $l$.},
affiliation = {Northwestern University Department of Mathematics 2033 Sheridan Road Evanston IL 60208-2730 (USA); Northwestern University Department of Mathematics 2033 Sheridan Road Evanston IL 60208-2730 (USA)},
author = {Calegari, Frank, Gee, Toby},
journal = {Annales de l’institut Fourier},
keywords = {Galois representations; automorphic representations; représentations galoisiennes; représentations automorphes; -adic Galois representation; cuspidal automorphic representation; totally real field},
language = {eng},
number = {5},
pages = {1881-1912},
publisher = {Association des Annales de l’institut Fourier},
title = {Irreducibility of automorphic Galois representations of $GL(n)$, $n$ at most $5$},
url = {http://eudml.org/doc/275430},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Calegari, Frank
AU - Gee, Toby
TI - Irreducibility of automorphic Galois representations of $GL(n)$, $n$ at most $5$
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 5
SP - 1881
EP - 1912
AB - Let $\pi $ be a regular, algebraic, essentially self-dual cuspidal automorphic representation of $\textrm{GL}_n({\mathbb{A}}_F)$, where $F$ is a totally real field and $n$ is at most $5$. We show that for all primes $l$, the $l$-adic Galois representations associated to $\pi $ are irreducible, and for all but finitely many primes $l$, the mod $l$ Galois representations associated to $\pi $ are also irreducible. We also show that the Lie algebras of the Zariski closures of the $l$-adic representations are independent of $l$.
LA - eng
KW - Galois representations; automorphic representations; représentations galoisiennes; représentations automorphes; -adic Galois representation; cuspidal automorphic representation; totally real field
UR - http://eudml.org/doc/275430
ER -

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