Hesselholt and Madsen (2004) define and study the (absolute, -typical) de Rham–Witt complex in mixed characteristic, where is an odd prime. They give as an example an elementary algebraic description of the de Rham–Witt complex over , . The main goal of this paper is to construct, for a perfect ring of characteristic , a Witt complex over with an algebraic description which is completely analogous to Hesselholt and Madsen’s description for . Our Witt complex is not isomorphic to the de Rham–Witt complex; instead we prove that, in each level, the de Rham–Witt complex over surjects onto our Witt complex, and that the kernel consists of all elements which are divisible by arbitrarily high powers of . We deduce an explicit description of for each . We also deduce results concerning the de Rham–Witt complex over certain -torsion-free perfectoid rings.
"On the $p$-typical de Rham–Witt complex over $W(k)$." Algebra Number Theory 13 (7) 1597 - 1631, 2019. https://doi.org/10.2140/ant.2019.13.1597