Vector bundles and local systems on non-Archimedean analytic spaces

非阿基米德解析空间上的向量丛和局部系统

• 批准号: 446443754
• 负责人: Professorin Dr. Annette Werner
• 金额: --
• 依托单位: Schwerpunkt Algebra und Geometrie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/446443754?language=en
• 关键词: Vector; bundles; local; systems; non

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.

本项目旨在更深入地理解纳拉西姆汉-塞沙德里和辛普森的经典书信的p元译本。PI和Christopher Deninger以前的工作在一个适当的光滑p-进系簇上引入了具有数值平坦约化的向量丛范畴，它可以与p-进并行传输的连续函子相联系。伍尔滕展示了如何在适当的刚性空间上重新解释和推广这种结构，并借助肖尔茨的Pro-etale网站。这个项目的目标有三个：我们想把这一观点推广到抛物型丛的p-进Narasimhan-Seshadri结果，我们计划利用肖尔茨的钻石理论来研究在适当的拉回后具有数值平坦约化的丛，最后我们计划攻击非零希格斯场的情况。