Kunneth formula for graded rings associated to K-theories of Rost motives

TL;DR

This paper investigates the structure of graded rings derived from K-theory of twisted flag varieties, explicitly studies the Kunneth map for Rost motives, and provides examples of nontrivial torsion in Chow rings.

Contribution

It introduces explicit analysis of the Kunneth map for Rost motives and demonstrates nontrivial torsion in Chow rings of certain varieties.

Findings

Explicit description of the Kunneth map for Rost motives

Identification of nonzero torsion in Chow rings

Examples illustrating the structure of gr(X)

Abstract

In this paper, we study the graded ring gr(X) defined by the K-theory of twisted flag variety X. In particular, Kunneth map from gr(R')(\otimes)gr(R') to gr(R) is studed explicitly for an original Rost motive R' and a generalized Rost motive R. Using this, we give an example that T(X)^2 is nonzero for the torsion ideal T(X) in the Chow ring CH(X).