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arXiv · 1609.04223

Galois representations for general symplectic groups

Arno Kret·Sug Woo Shin
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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.

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Arno Kret, Sug Woo Shin. 2016-09-14. Galois representations for general symplectic groups. https://arxiv.org/abs/1609.04223

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