Classifying spaces of algebraic groups and A1-homotopy theory.

本文拟从动机同伦理论的角度系统地研究代数群G的分类空间，以及与G-等变动机同伦理论有关的一些自然问题.例如，在我们证明了弗里德兰德-米尔诺猜想之后，我们可以攻击关于点群G（F）对于不一定代数闭域F的同调的新结果。另一个（相关）方向是关注塞尔的代数伽罗瓦上同调。我们确实有一个精确的猜想，这意味着大多数这些类型的acquitures，最重要的是一个是迄今为止未触及的，和一个新的方法来解决它。更一般地说，我们有兴趣在运输经典问题（等变）同伦理论motivic同伦理论。 像亚当斯猜想，西格尔猜想，各种结构配边的行为，比如，首先，正交配边。

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.