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

Abstract

For a smooth scheme X of pure dimension d over a field k and an effective Cartier divisor D⊂X whose support is a simple normal crossing divisor, we construct a cycle class mapcycX|D:CH0(X|D)→HNisd(X,KdM(OX,ID)) from the Chow group of zero-cycles with modulus to the cohomology of the relative Milnor K-sheaf.