Galois representations for even general special orthogonal groups
Abstract
We prove the existence of $\mathrm{GSpin}_{2n}$valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasisplit 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.08408
 Bibcode:
 2020arXiv201008408K
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Representation Theory