Algebraic groups and motives of projective homogeneous varieties of outer type

外型射影齐次簇的代数群和母题

• 批准号: 432236229
• 负责人: Professor Dr. Nikita Geldhauser
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/432236229?language=en
• 关键词: Algebraic; groups; motives; projective; homogeneous

The concept of motive is fundamental in modern algebraic geometry. Originally it was introduced by Alexander Grothendieck as an attempt to unify cohomology theories. Meanwhile motives became one of the main languages in algebraic geometry to formulate and to solve its problems. The subject of our investigations are algebraic groups over arbitrary fields with a focus on groups of outer type, homogeneous varieties, and their Chow motives. Our main goals include motivic decompositions of homogeneous varieties, discrete motivic invariants, study of algebraic cycles on homogeneous varieties and cohomological invariants of groups and torsors.

动机的概念是现代代数几何的基本概念。它最初是由亚历山大·格罗滕迪克（Alexander Grothendieck）引入的，目的是为了统一上同调理论。同时，动机成为代数几何中表述和解决代数几何问题的主要语言之一。我们研究的主题是任意域上的代数群，重点是外型群、齐次群及其周氏动机。我们的主要目标包括齐次变量的动机分解、离散动机不变量、齐次变量上的代数循环以及群和环的上同调不变量的研究。