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We show that de Rham--Witt forms are naturally isomorphic to $p$-typicalcurves on $p$-adic Tate twists, which revisits a question of Artin--Mazurpursued in the earlier work of Bloch and Kato. We show this by more generallyequipping a related result of Hesselholt on topological cyclic homology withthe motivic filtrations introduced by Bhatt--Morrow--Scholze.

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