Galois representations for general symplectic groups
Abstract
We prove the existence of GSpin-valued Galois representations corresponding to cohomological cuspidal automorphic representations of general symplectic groups over totally real number fields under the local hypothesis that there is a Steinberg component. This confirms the Buzzard-Gee conjecture on the global Langlands correspondence in new cases. As an application we complete the argument by Gross and Savin to construct a rank seven motive whose Galois group is of type G_2 in the cohomology of Siegel modular varieties of genus three. Under some additional local hypotheses we also show automorphic multiplicity one as well as meromorphic continuation of the spin L-functions.
Cite
@article{arxiv.1609.04223,
title = {Galois representations for general symplectic groups},
author = {Arno Kret and Sug Woo Shin},
journal= {arXiv preprint arXiv:1609.04223},
year = {2022}
}
Comments
Appeared in Journal of the European Mathematical Society. This final version incorporates an Erratum for the paper listed in section 16 of arXiv:2010.08408 (version of October 2020). This erratum is also incorporated in the published JEMS version. Both the JEMS version and this arxiv version are the most recent versions of the paper (as of June 14th 2022)