# Galois representations for even general special orthogonal groups

@article{Kret2020GaloisRF, title={Galois representations for even general special orthogonal groups}, author={Arno Kret and Sug Woo Shin}, journal={arXiv: Number Theory}, year={2020} }

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… Expand

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