Overconvergent Chern Classes and Higher Cycle Classes

TL;DR

This paper constructs integral and higher cycle classes for smooth varieties over fields of characteristic p>0 using overconvergent de Rham-Witt complexes, extending rigid Chern classes with a comparison theorem.

Contribution

It introduces a new construction of Chern and cycle classes with overconvergent coefficients, compatible with existing rigid classes, based on cycle modules theory.

Findings

Construction of integral Chern classes in overconvergent de Rham-Witt complexes

Compatibility with rigid Chern classes by Petrequin

A comparison theorem for quasi-projective varieties

Abstract

The goal of this work is to construct integral Chern classes and higher cycle classes for a smooth variety over a perfect field of characteristic p>0 that are compatible with the rigid Chern classes defined by Petrequin. The Chern classes we define have coefficients in the overconvergent de Rham-Witt complex of Davis, Langer and Zink and the construction is based on the theory of cycle modules discussed by Rost. We prove a comparison theorem in the case of a quasi-projective variety.