论文标题
在自旋组中重视的动机加洛瓦表示
Motivic Galois representations valued in Spin groups
论文作者
论文摘要
令$ m $为一个整数，以至于$ m \ geq 7 $和$ m \ equiv 0,1,7 \ mod 8 $。我们严格构建$γ_ {\ Mathbb Q} \ to \ Mathrm {spin} _M（\ overline {\ Mathbb q} _l）\ xrightArrow {\ xrightArrow {\ \ spinrm {spin}}} _ {潜在的自动形态和动机。作为一个应用程序，我们证明了$ \ mathbb f_p $ - 旋转组点的逆galois问题。对于Odd $ m $，我们将示例与A. Kret和S. W. Shin的作品进行了比较，后者研究了以$ \ Mathrm {Spin} _M $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ \ MATHRM {spin}的自动形态galois表示形式进行了比较。
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 $Γ_{\mathbb Q} \to \mathrm{Spin}_m(\overline{\mathbb Q}_l) \xrightarrow{\mathrm{spin}} \mathrm{GL}_N(\overline{\mathbb Q}_l)$ 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. Shin, which studies automorphic Galois representations valued in $\mathrm{Spin}_m$.
