Exponential motivic homotopy theory, foliations and applications

指数本征同伦理论、叶状结构及应用

• 批准号: 405466915
• 负责人: Dr. Simon Pepin Lehalleur
• 金额: --
• 依托单位: Institute for Mathematics, Astrophysics and Particle Physics
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/405466915?language=en
• 关键词: Exponential; motivic; homotopy; theory; foliations

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.

这是在SPP 1786中提交给DFG的提案。这里描述的项目包括两个相关的主题。第一个是指数动机同伦理论的构建和探索，动机同伦理论的变种品种的潜力。第二部分围绕叶理的几何和同伦理论和高等微分伽罗瓦理论，及其在动机和代数循环研究中的应用。指数连接和扭曲的德拉姆复杂发挥了核心作用，在这两个领域。