تقرير
Local constancy of pro-unipotent Kummer maps
| العنوان: | Local constancy of pro-unipotent Kummer maps |
|---|---|
| المؤلفون: | Betts, L. Alexander |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Number Theory, Primary: 11G25, Secondary: 14G22 |
| الوصف: | 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 \'etale-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. Comment: 31 pages, comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2203.03701 |
| رقم الأكسشن: | edsarx.2203.03701 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |