Motivic Galois representations valued in Spin groups

2020/06/05 by Tang, Shiang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.03585

Abstract

Let m be an integer such that m ≥ 7 and m ≡ 0,1,7 \mod 8. We construct strictly compatible systems of representations of Γ_{\mathbb Q} → Spin_m(\mathbb Q_l) \xrightarrowspin GL_N(\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. Shin, which studies automorphic Galois representations valued in Spin_m.

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