A new approach to de Rham-Witt complexes, after Bhatt, Lurie, and Mathew (Q2075254)

This paper is a report on [\textit{B. Bhatt} et al., Revisiting the de Rham-Witt complex. Paris: Société Mathématique de France (SMF) (2021; Zbl 1478.14038)]. As the author said: ``My aim ... is 4-fold: -- put [loc. cit.] in a broader historical perspective; -- give a short and (as much as possible) self-contained summary of its basic definitions, constructions, and properties; -- discuss examples; -- discuss open questions and perspectives.'' Since this report was written before the final publication of [loc. cit.], a few proofs presented here are different from the published version of [loc. cit.]. These old proofs are sometimes more direct, if slightly less conceptual, than those appeared in the published version.