A motivic construction of the de Rham-Witt complex

TL;DR

This paper generalizes the theory of reciprocity sheaves to include $Q$-divisors and constructs the de Rham-Witt complex using motivic methods, extending previous motivic constructions of algebraic invariants.

Contribution

It introduces a new framework for reciprocity sheaves with $Q$-divisors and provides a motivic construction of the de Rham-Witt complex, linking it to Milnor K-theory.

Findings

Generalization of reciprocity sheaves to $Q$-divisors

Motivic construction of the de Rham-Witt complex

Connection to Milnor K-theory

Abstract

The theory of reciprocity sheaves due to Kahn-Saito-Yamazaki is a powerful framework to study invariants of smooth varieties via invariants of pairs $(X,D)$ of a variety $X$ and a divisor $D$. We develop a generalization of this theory where $D$ can be a $\mathbb{Q}$-divisor. As an application, we provide a motivic construction of the de Rham-Witt complex, which is analogous to the motivic construction of the Milnor $K$-theory due to Suslin-Voevodsky.