# Motivic Galois representations valued in Spin groups

@article{Tang2020MotivicGR,
title={Motivic Galois representations valued in Spin groups},
author={Shiang Tang},
journal={arXiv: Number Theory},
year={2020}
}
• Shiang Tang
• Published 2020
• Mathematics
• arXiv: Number Theory
Let $m$ be an integer such that $m \geq 7$ and $m \equiv 0,1,7 \mod 8$. We construct strictly compatible systems of representations of $\Gamma_{\mathbb Q} \to \mathrm{Spin}_m(\overline{\mathbb Q}_l) \xrightarrow{\mathrm{spin}} \mathrm{GL}_N(\overline{\mathbb Q}_l)$ that is potentially automorphic and motivic. As an application, we prove instances of the inverse Galois problem for the $\mathbb F_p$--points of the spin groups. For odd $m$, we compare our examples with the work of A. Kret and S. W… Expand

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