Rost nilpotence and free theories

TL;DR

This paper proves that Rost nilpotence holds for projective homogeneous varieties within certain coherent cohomology theories, including algebraic cobordism and free theories, under the condition of generic constancy.

Contribution

It establishes the Rost nilpotence principle for projective homogeneous varieties in the context of coherent cohomology theories that are generically constant, expanding its applicability.

Findings

Rost nilpotence holds for projective homogeneous varieties in certain cohomology theories.

Algebraic cobordism and free theories satisfy the conditions for the principle.

The paper introduces the concept of coherent cohomology theories and proves their relevance to Rost nilpotence.

Abstract

We introduce coherent cohomology theories h_* and prove that if such a theory is moreover generically constant then the Rost nilpotence principle holds for projective homogeneous varieties in the category of h_*-motives. Examples of such theories are algebraic cobordism and its descendants the free theories.