Overconvergent chern classes and higher cycle classes

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.