Integrality of the Chern character in small codimension

TL;DR

This paper proves an integrality property of the Chern character in Chow groups and constructs Steenrod operations modulo p, with applications to algebraic variety correspondences.

Contribution

It introduces an integrality property of the Chern character and constructs Steenrod operations on Chow groups over arbitrary fields.

Findings

Established integrality of the Chern character in Chow groups.

Constructed p-1 first homological Steenrod operations modulo p.

Applied results to study correspondences between algebraic varieties.

Abstract

We prove an integrality property of the Chern character with values in Chow groups. As a consequence we obtain, for a prime number p, a construction of the p-1 first homological Steenrod operations on Chow groups modulo p and p-primary torsion, over an arbitrary field. We provide applications to the study of correspondences between algebraic varieties.