Cycle class maps for Chow groups of zero-cycles with modulus

TL;DR

This paper constructs a cycle class map linking Chow groups of zero-cycles with modulus to top cohomology of relative Milnor K-sheaves for smooth schemes with normal crossing divisors, advancing the understanding of algebraic cycles with modulus.

Contribution

It introduces a new cycle class map for zero-cycles with modulus on smooth schemes with normal crossing divisors, connecting Chow groups to Milnor K-theory cohomology.

Findings

Established the cycle class map for zero-cycles with modulus.

Connected Chow groups with Milnor K-sheaf cohomology.

Provided tools for studying algebraic cycles with modulus.

Abstract

For a quasi-projective smooth scheme X of pure dimension d over a field k and an effective Cartier divisor D on X whose support is a simple normal crossing divisor, we construct a cycle class map from the Chow group of zero-cycles with modulus to the top cohomology of the dth relative Milnor K-sheaf.