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.

我们建议从动机同伦理论的角度系统地研究代数群G的分类空间，以及G-等变动机同伦理论的一些自然相关问题。例如，在证明弗里德兰德-米尔诺猜想之后，我们可以攻击不一定是代数闭域 F 的点群 G(F) 同调性的新结果。另一个（相关）方向涉及伽罗瓦上同调中的塞尔猜想。我们确实有一个精确的猜想，它暗示了大多数此类猜想，最重要的是迄今为止尚未触及的猜想，以及解决它的新方法。更一般地说，我们感兴趣的是将（等变）同伦理论的经典问题转移到动机同伦理论。 就像亚当斯猜想、西格尔猜想一样，各种结构化共边主义的行为，首先是正交共边主义。