Automorphic realization of residual Galois representations

Guralnick, Robert, Harris, Michael, and Katz, Nicholas M.. "Automorphic realization of residual Galois representations." Journal of the European Mathematical Society 012.4 (2010): 915-937. <http://eudml.org/doc/277438>.

@article{Guralnick2010,
abstract = {We show that it is possible in rather general situations to obtain a finite-dimensional modular representation $\rho $ of the Galois group of a number field $F$ as a constituent of one of the modular Galois representations attached to automorphic representations of a general linear group over $F$, provided one works “potentially.” The proof is based on a close study of the monodromy of the Dwork family of Calabi–Yau hypersurfaces; this in turn makes use of properties of rigid local systems and the classification of irreducible subgroups of finite classical groups with certain sorts of generators.},
author = {Guralnick, Robert, Harris, Michael, Katz, Nicholas M.},
journal = {Journal of the European Mathematical Society},
keywords = {Galois representations; automorphy; hypergeometric local systems; Galois representations; automorphy; hypergeometric local systems},
language = {eng},
number = {4},
pages = {915-937},
publisher = {European Mathematical Society Publishing House},
title = {Automorphic realization of residual Galois representations},
url = {http://eudml.org/doc/277438},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Guralnick, Robert
AU - Harris, Michael
AU - Katz, Nicholas M.
TI - Automorphic realization of residual Galois representations
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 4
SP - 915
EP - 937
AB - We show that it is possible in rather general situations to obtain a finite-dimensional modular representation $\rho $ of the Galois group of a number field $F$ as a constituent of one of the modular Galois representations attached to automorphic representations of a general linear group over $F$, provided one works “potentially.” The proof is based on a close study of the monodromy of the Dwork family of Calabi–Yau hypersurfaces; this in turn makes use of properties of rigid local systems and the classification of irreducible subgroups of finite classical groups with certain sorts of generators.
LA - eng
KW - Galois representations; automorphy; hypergeometric local systems; Galois representations; automorphy; hypergeometric local systems
UR - http://eudml.org/doc/277438
ER -