de Rham-Witt sheaves via algebraic cycles

TL;DR

This paper establishes a cycle-theoretic description of big de Rham-Witt sheaves via additive higher Chow groups, providing new insights into their structure and applications in algebraic geometry.

Contribution

It introduces a Zariski sheaf of pro-differential graded algebras from additive higher Chow groups and proves its isomorphism to big de Rham-Witt complexes.

Findings

Additive higher Chow groups induce a sheaf of pro-differential graded algebras.

Milnor range is isomorphic to the Zariski sheaf of big de Rham-Witt complexes.

Provides explicit cycle-theoretic descriptions with several applications.

Abstract

We show that the additive higher Chow groups of regular schemes over a field induce a Zariski sheaf of pro-differential graded algebras, whose Milnor range is isomorphic to the Zariski sheaf of big de Rham-Witt complexes. This provides an explicit cycle-theoretic description of the big de Rham-Witt sheaves. Several applications are derived.