Cohomological invariants of algebraic groups and the Morava K-theory

TL;DR

This paper explores the relationships between cohomological invariants of algebraic groups, such as Tits algebras and Rost invariants, and Morava K-theory, along with oriented cohomology theories and Rost motives.

Contribution

It introduces new connections between algebraic group invariants and Morava K-theory, expanding the understanding of cohomological invariants in algebraic geometry.

Findings

Relates Tits algebras and Rost invariants to Morava K-theory

Discusses oriented cohomology theories of affine varieties

Analyzes Rost motives across different cohomology theories

Abstract

In the present article we discuss different approaches to cohomological invariants of algebraic groups over a field. We focus on the Tits algebras and on the Rost invariant and relate them to the Morava K-theory. Furthermore, we discuss oriented cohomology theories of affine varieties and the Rost motives for different cohomology theories in the sense of Levine-Morel.