A remark on the Rost Nilpotence Principle

TL;DR

This paper explores a weaker form of the Rost Nilpotence Principle, demonstrating that its validity over all smooth projective schemes implies the full principle over characteristic zero fields, and corrects a previous proof.

Contribution

It introduces a weak version of the Rost Nilpotence Principle and proves its implication for the full principle over characteristic zero fields, also correcting a prior lemma.

Findings

Weak version of Rost Nilpotence Principle established

Implication shown for all smooth projective schemes over characteristic zero fields

Previous lemma correction provided

Abstract

We consider a weak version of the Rost Nilpotence Principle. For characteristic zero fields k, we show that if it holds for all smooth projective schemes over k, then the Rost Nilpotence Principle does also. We also correct the proof of a lemma in arXiv:1807.08163(3).