The generalized de Rham-Witt complex over a field is a complex of zero-cycles

Abstract

Bloch and Esnault defined additive higher Chow groups with modulus m on the level of zero cycles over a field k denoted by CH n ((A 1 k , (m + 1){0}), n − 1), n, m ≥ 1. Bloch and Esnault prove CH n ((A 1 k , 2{0}), n − 1) ∼ = Ω n−1 k/Z . In this paper we generalize their result and prove that the additive Chow groups with higher modulus form a generalized Witt complex over k and are as such isomorphic to the generalized de Rham-Witt complex of Bloch-Deligne-Hesselholt-Illusie-Madsen.

Deformations of Bloch groups and Aomoto dilogarithms in characteristic p

“…For the approach to infinitesimal motivic cohomology, based on additive Chow groups, we refer the reader to the works of Park [17] and Rülling [18].…”

Additive polylogarithms and their functional equations

“…For infinitesimal motivic cohomology in the context of additive Chow groups we refer the reader to [5,18,16,19]. …”

On the additive dilogarithm

“…First, we mention the work of J. Park [2007], which gives an additive Chow theoretic description of the additive dilogarithm of Bloch and Esnault, and the work of K. Rülling [2007], which proves that the complex of additive Chow groups with modulus (not necessarily of 2) has the expected cohomology groups on the level of zero cycles.…”