• Corpus ID: 223953370

Galois representations for even general special orthogonal groups

  title={Galois representations for even general special orthogonal groups},
  author={Arno Kret and Sug Woo Shin},
  journal={arXiv: Number Theory},
  • A. KretS. Shin
  • Published 16 October 2020
  • Mathematics
  • arXiv: Number Theory
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… 
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