Rost nilpotence and higher unramified cohomology

TL;DR

This paper introduces a new approach using higher unramified cohomology to prove the Rost nilpotence principle for specific low-dimensional varieties over perfect fields.

Contribution

It develops a novel method connecting higher unramified cohomology with Rost nilpotence, proving the principle for certain three-dimensional varieties.

Findings

Proves Rost nilpotence for some varieties of dimension ≤ 3

Establishes a link between unramified cohomology and nilpotence

Provides a new technique for algebraic cycle theory

Abstract

We develop an approach to proving the Rost nilpotence principle involving higher unramified cohomology. We use this to prove the principle for certain varieties of dimension $\leq 3$ over a perfect field.