Zero-cycles with modulus associated to hyperplane arrangements on affine spaces

Abstract

For a hyperplane arrangement on the affine n-space over k, we define and study a group of zero-cycles relative to , which is closely related to the relative Chow group of M. Kerz and S. Saito. We compute our cycle groups for a special kind of hyperplane arrangements, called polysimplicial spheres. We prove that they are isomorphic to the Milnor K-groups , similar to the theorem of Nesterenko-Suslin-Totaro. Using this result, we show that the Kerz-Saito relative Chow group does not necessarily vanish for , contrary to the result of Krishna-Park that for and , the group does vanish when k is a field of characteristic 0.