Vector bundles and local systems on non-Archimedean analytic spaces

该项目旨在更深入地理解Narasimhan-Seshadri和Simpson的经典通信的p进版本。PI先前与Christopher Deninger一起的工作引入了在适当的，光滑的p进变换上具有数值平坦化的向量束的类别，p进平行移动的连续函子可以与之相关联。w<s:1> rthen在Scholze的pro- tale site的帮助下，展示了如何在适当的刚性空间上重新解释和概括这种结构。本项目的目标有三个：我们希望将这一观点推广到抛物线束的p进Narasimhan-Seshadri结果，我们计划利用Scholze的钻石理论来研究适当回拉后具有数值平坦化的束，最后我们计划攻击非消失希格斯场的情况。

This project aims a deeper understanding of p-adic versions of the classical correspondences of Narasimhan-Seshadri and Simpson. Previous work of the PI together with Christopher Deninger introduces the category of vector bundles with numerically flat reduction on a proper, smooth p-adic variety to which a continuous functor of p-adic parallel transport can be associated. Würthen has shown how to reinterpret and generalize this construction on proper rigid spaces with the help of Scholze's pro-etale site. The goal of the proposed project is threefold: We want to generalize this point of view to a p-adic Narasimhan-Seshadri result for parabolic bundles, we plan to make use of Scholze's theory of diamonds to study bundles with numerically flat reduction after proper pullback, and finally we plan to attack the case of non-vanishing Higgs field.