On the de Rham–Witt Complex over Perfectoid Rings

Abstract Fix an odd prime $p$. The results in this paper are modeled after work of Hesselholt and Hesselholt–Madsen on the $p$-typical absolute de Rham–Witt complex mixed characteristic. We have two primary results. 1st result is exact sequence that describes kernel restriction map over $A$, where $A$ ring integers algebraic extension $\textbf{Q}_p$ or a $p$-torsion-free perfectoid ring. 2nd description $p$-power torsion (and related objects) containing compatible system roots unity. Both these analogous to Madsen. Our main contribution their certain rings. also provide proofs results, whereas Madsen used techniques from topology.