Chern classes with modulus

TL;DR

This paper develops a new construction of Chern classes using relative K-theory for modulus pairs, linking it to relative motivic cohomology, with applications to henselian DVRs.

Contribution

It introduces a novel method to construct Chern classes from relative K-theory of modulus pairs, connecting it to relative motivic cohomology.

Findings

Constructed Chern classes from relative K-theory of modulus pairs.

Linked Chern classes to relative motivic cohomology.

Applied theory to relative motivic cohomology of henselian DVRs.

Abstract

In this paper, we construct Chern classes from the relative $K$-theory of modulus pairs to the relative motivic cohomology defined by Binda-Saito. An application to relative motivic cohomology of henselian dvr is given.