Rationality of cycles on function field of exceptional projective homogeneous varieties

TL;DR

This paper investigates the rationality of algebraic cycles on function fields of certain exceptional projective homogeneous varieties, establishing a comparison with their rationality over the base field across all characteristics.

Contribution

It provides a new comparison result for algebraic cycle rationality on varieties associated with groups of type F4 and E8, extending understanding across different characteristics.

Findings

Rationality of cycles over function fields relates to their rationality over the base field.

The result applies to varieties under linear algebraic groups of type F4 and E8.

The comparison holds in any characteristic.

Abstract

In this article we prove a result comparing rationality of algebraic cycles over the function field of a projective homogeneous variety under a linear algebraic group of type $F_4$ or $E_8$ and over the base field, which can be of any characteristic.