论文标题
亲联合Kummer地图的当地恒定
Local constancy of pro-unipotent Kummer maps
论文作者
论文摘要
Kim-Tamagawa的定理是，$ \ Mathbb Q_ \ ell $ -pro-pro-nipotent kummer地图与光滑的投影曲线$ y $相关的$ \ mathbb q_p $在$ \ ell \ ell \ ell \ neq p $时是本地常数。本文建立了这一结果的两个概括。首先，我们将Kim-Tamagawa定理扩展到$ y $都是任何维度的平滑品种的情况。其次，我们在任意维度中再次制定并证明了Kim-Tamagawa定理的类似物。在证明后者的过程中，我们提供了使用Scholze和diao-lan-liu-Zhu方法的典型de rham比较定理，用于亲合物基本群。这扩展了Vologodsky对基本类固醇的某些截断证明的比较定理。
It is a theorem of Kim-Tamagawa that the $\mathbb Q_\ell$-pro-unipotent Kummer map associated to a smooth projective curve $Y$ over a finite extension of $\mathbb Q_p$ is locally constant when $\ell\neq p$. The present paper establishes two generalisations of this result. Firstly, we extend the Kim-Tamagawa Theorem to the case that $Y$ is a smooth variety of any dimension. Secondly, we formulate and prove the analogue of the Kim-Tamagawa Theorem in the case $\ell = p$, again in arbitrary dimension. In the course of proving the latter, we give a proof of an étale-de Rham comparison theorem for pro-unipotent fundamental groupoids using methods of Scholze and Diao-Lan-Liu-Zhu. This extends the comparison theorem proved by Vologodsky for certain truncations of the fundamental groupoids.
