Exponential motivic homotopy theory, foliations and applications

这是在SPP 1786范围内提交给DFG的一项提案。这里介绍的项目由两个相关主题组成。首先是指数基元同伦理论的构建和探索，指数基元同伦理论是具有势的变种的基元同伦理论的变体。第二部分是关于叶层的几何同伦理论和高阶Galois微分理论，以及它在动机和代数圈研究中的应用。指数连接和扭曲的德罗姆复合体在这两个领域都发挥着核心作用。

This is a proposal submitted to the DFG within the SPP 1786. The project described here consists of two related topics. The first is the construction and exploration of exponential motivic homotopy theory, a variant of motivic homotopy theory for varieties with potentials. The second is centered around the geometric and homotopical theory of foliations and higher differential Galois theory, and its application to the study of motives and algebraic cycles. Exponential connections and the twisted de Rham complex play a central role in both areas.