Algebra/Topology seminar

Speaker: Ko Aoki

Tilte: Computations with higher motives

Abstract: The theory of (1-)motives in arithmetic geometry aims to establish a universal cohomology theory for algebraic varieties. By shifting our focus from cohomology theories to coefficient theories, we arrive at the (∞,2)-category of 2-motives. In the first half of this talk, I will explain this without being too technical, starting with a review of classical motives. I will then present some computations, which show contrasts with the 1-motivic case and illustrate an advantage of this higher categorical approach. Finally, I will briefly discuss future plans to address the challenges that arise in this context.