$p$-typical curves on $p$-adic Tate twists and de Rham-Witt forms

TL;DR

This paper establishes a natural isomorphism between de Rham--Witt forms and p-typical curves on p-adic Tate twists, connecting several advanced concepts in algebraic geometry and number theory.

Contribution

It provides a new conceptual link between de Rham--Witt forms and p-typical curves on p-adic Tate twists, answering a long-standing question of Artin--Mazur.

Findings

Proves the isomorphism between de Rham--Witt forms and p-typical curves.

Extends Hesselholt's results on topological cyclic homology with motivic filtrations.

Addresses a question from 1977 by Artin--Mazur.

Abstract

We show that de Rham--Witt forms are naturally isomorphic to $p$-typical curves on $p$-adic Tate twists, which answers a question of Artin--Mazur from 1977 pursued in the earlier work of Bloch and Kato. We show this by more generally equipping a related result of Hesselholt on topological cyclic homology with the motivic filtrations introduced by Bhatt--Morrow--Scholze.