Chern classes from Morava K-theories to Chow groups

TL;DR

This paper computes the structure of operations from algebraic Morava K-theory to Chow groups, revealing a formal power series ring generated by specific characteristic classes with a Cartan formula.

Contribution

It explicitly describes the ring of unstable operations from Morava K-theory to Chow groups, including generators and relations, extending understanding of these cohomological operations.

Findings

The ring of operations is a formal power series ring.

Generators satisfy a Cartan-type formula.

Provides explicit description of these operations.

Abstract

In this paper we calculate the ring of unstable (possibly non-additive) operations from algebraic Morava K-theory K(n) to Chow groups with $\mathbb{Z}_{(p)}$-coefficients. More precisely, we prove that it is a formal power series ring on generators $c_i:K(n)\rightarrow CH^i \otimes \mathbb{Z}_{(p)}$, which satisfy a Cartan-type formula.