Oriented cohomology theories and equivariant motives

• Applicant: Professor Dr. Nikita Geldhauser
• Subject Area: Mathematics
• Term: from 2015 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 268769163

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.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1786: Homotopy Theory and Algebraic Geometry