Oriented cohomology theories and equivariant motives

有向上同调理论的概念在代数拓扑中是众所周知的。在代数几何中，列文、莫雷尔、帕宁和斯米尔诺夫引入并系统地研究了它。此外，有向上同调理论还存在一个等变版本。与Grothendieck对Chow动机的构造类似，我们可以根据任何定向上同论（普通或等变）来定义动机的范畴。动机在理解方案的上同调和代数几何本身中起着中心作用。有大量的文献致力于经典的周动机（也是由于申请人），但到目前为止，关于任意取向上同理论的动机结构的结果很少。在这方面取得进展是本项目的目标之一。

The concept of an oriented cohomology theory is well known in algebraic topology. In algebraic geometry it was introduced and systematically studied by Levine, Morel, Panin and Smirnov. Moreover, there exist an equivariant version of oriented cohomology theories. Similar to Grothendieck's construction of Chow motives, one can define the category of motives with respect to any oriented cohomology theory (ordinary or equivariant). Motives play a central role in understanding of the cohomologies of schemes and in the algebraic geometry by itself. There exists a broad literature devoted to classical Chow motives (also due to the applicant), but so far there are very few results about the structure of motives with respect to arbitrary oriented cohomology theories. To make progress on this is one of the goals of the present project.