Roy Joshua
The Ohio State University
Title
Motivic Euler characteristic and the transfer
Abstract
This concerns the following conjecture of Fabien Morel. Given a linear algebraic group G defined over a field k, with a maximal torus T, the conjecture was that a suitable form of the Euler Characteristic of G/N(T), where N(T) is the normalizer of T in G, is 1, when viewed as a class in the Grothendieck-Witt group of the field k. In a paper in 2023, together with P. Pelaez, we settled this conjecture in the affirmative for split groups G, provided the field k has a square root of -1. We also showed that this implies the same Euler characteristic is a unit in general.
This has numerous applications to splitting in various forms of Borel-style equivariant cohomology theories, for example, equivariant K-theory, equivariant (higher) Chow groups, equivariant Brauer groups etc., and greatly facilitates the computation of all such equivariant cohomology theories.
The talk will sketch a proof of the conjecture and outline some of the applications.
