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

Abstract

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