1 results
GALOIS REPRESENTATIONS FOR EVEN GENERAL SPECIAL ORTHOGONAL GROUPS
- Part of
-
- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 23 / Issue 5 / September 2024
- Published online by Cambridge University Press:
- 13 December 2023, pp. 1959-2050
- Print publication:
- September 2024
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
We prove the existence of
$\mathrm {GSpin}_{2n}$-valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasi-split forms of 
${\mathrm {GSO}}_{2n}$ under the local hypotheses that there is a Steinberg component and that the archimedean parameters are regular for the standard representation. This is based on the cohomology of Shimura varieties of abelian type, of type 
$D^{\mathbb {H}}$, arising from forms of 
${\mathrm {GSO}}_{2n}$. As an application, under similar hypotheses, we compute automorphic multiplicities, prove meromorphic continuation of (half) spin L-functions and improve on the construction of 
${\mathrm {SO}}_{2n}$-valued Galois representations by removing the outer automorphism ambiguity.
