We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Galois representations for general symplectic groups.
- Authors
Kret, Arno; Sug Woo Shin
- 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 7 motive whose Galois group is of type G2 in the cohomology of Siegel modular varieties of genus 3. Under some additional local hypotheses we also show automorphic multiplicity 1 as well as meromorphic continuation of the spin L-functions.
- Subjects
GALOIS theory; SYMPLECTIC groups; AUTOMORPHIC functions; REAL numbers; MULTIPLICITY (Mathematics)
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2023, Vol 25, Issue 1, p75
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1179