Automorphy for some l-adic lifts of automorphic mod l Galois representations

Laurent Clozel; Michael Harris; Richard Taylor

Publications Mathématiques de l'IHÉS (2008)

  • Volume: 108, page 1-181
  • ISSN: 0073-8301

Abstract

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We extend the methods of Wiles and of Taylor and Wiles from GL2 to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), minimally ramified, l-adic lifts of certain automorphic mod l Galois representations of any dimension. We also make a conjecture about the structure of mod l automorphic forms on definite unitary groups, which would generalise a lemma of Ihara for GL2. Following Wiles’ method we show that this conjecture implies that our automorphy lifting theorem could be extended to cover lifts that are not minimally ramified.

How to cite

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Clozel, Laurent, Harris, Michael, and Taylor, Richard. "Automorphy for some l-adic lifts of automorphic mod l Galois representations." Publications Mathématiques de l'IHÉS 108 (2008): 1-181. <http://eudml.org/doc/274357>.

@article{Clozel2008,
abstract = {We extend the methods of Wiles and of Taylor and Wiles from GL2 to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), minimally ramified, l-adic lifts of certain automorphic mod l Galois representations of any dimension. We also make a conjecture about the structure of mod l automorphic forms on definite unitary groups, which would generalise a lemma of Ihara for GL2. Following Wiles’ method we show that this conjecture implies that our automorphy lifting theorem could be extended to cover lifts that are not minimally ramified.},
author = {Clozel, Laurent, Harris, Michael, Taylor, Richard},
journal = {Publications Mathématiques de l'IHÉS},
language = {eng},
pages = {1-181},
publisher = {Springer-Verlag},
title = {Automorphy for some l-adic lifts of automorphic mod l Galois representations},
url = {http://eudml.org/doc/274357},
volume = {108},
year = {2008},
}

TY - JOUR
AU - Clozel, Laurent
AU - Harris, Michael
AU - Taylor, Richard
TI - Automorphy for some l-adic lifts of automorphic mod l Galois representations
JO - Publications Mathématiques de l'IHÉS
PY - 2008
PB - Springer-Verlag
VL - 108
SP - 1
EP - 181
AB - We extend the methods of Wiles and of Taylor and Wiles from GL2 to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), minimally ramified, l-adic lifts of certain automorphic mod l Galois representations of any dimension. We also make a conjecture about the structure of mod l automorphic forms on definite unitary groups, which would generalise a lemma of Ihara for GL2. Following Wiles’ method we show that this conjecture implies that our automorphy lifting theorem could be extended to cover lifts that are not minimally ramified.
LA - eng
UR - http://eudml.org/doc/274357
ER -

References

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Citations in EuDML Documents

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  1. Frank Calegari, Toby Gee, Irreducibility of automorphic Galois representations of , at most
  2. Gaëtan Chenevier, On the infinite fern of Galois representations of unitary type

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