Classifying spaces of algebraic groups and A1-homotopy theory.

代数群的分类空间和 A1-同伦理论。

• 批准号: 245979342
• 负责人: Professor Dr. Fabien Morel
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/245979342?language=en
• 关键词: Classifying; spaces; algebraic; groups; A1

We propose to study in a systematic way the classifyings spaces of algebraic groups G from the point of view of motivic homotopy theory, as well as some naturally related problems of G-equivariant motivic homotopy theory. For instance following our proof of the Friedlander-Milnor conjecture, we may attack new results on the homology of groups of points G(F) for not necessarily algebraically closed fields F. Another (related) direction is concerned with Serre's conjectures in Galois cohomology. We do have a precise conjecture that implies most of these type of conjectures, most importantly the one which is up to now untouched, and a new approach to settle it. More generally we are interested in transporting classical problems of (equivariant) homotopy theory to motivic homotopy theory. Like the Adams conjecture, the Segal conjecture, the behaviour of various structured cobordism like, to start with, the orthogonal cobordism.

我们建议以系统的方式研究代数群体G的分类空间，从动机同义理论的角度以及G-Equivariant动机同型理论的一些自然相关问题。例如，遵循弗里德兰德 - 米尔诺（Friedlander-Milnor）的猜想的证明，我们可能会攻击G（F）组的同源性的新结果，因为不一定是代数封闭的场F。另一个（相关）方向与Serre在Galois共同体中的猜想有关。我们确实有一个精确的猜想，暗示了大多数此类猜想，最重要的是，现在已经不受欢迎的猜想，以及一种解决问题的新方法。更普遍地，我们有兴趣将（e象）同质理论的经典问题传播到动机同义理论。 像亚当斯的猜想一样，塞加尔的猜想，各种结构化的恢复主义的行为，例如正交恢复。