/sci/ - Science & Math

https://arxiv.org/pdf/1805.05501
>Revisiting the de Rham-Witt complex
>Bhargav Bhatt, Jacob Lurie, Akhil Mathew
>(Submitted on 15 May 2018)
>The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic p.
>We introduce a category of cochain complexes equipped with an endomorphism F (of underlying graded abelian groups) satisfying dF=pFd, whose homological algebra we study in detail. To any such object satisfying an abstract analog of the Cartier isomorphism, an elementary homological process associates a generalization of the de Rham-Witt construction. Abstractly, the homological algebra can be viewed as a calculation of the fixed points of the Berthelot-Ogus operator Lηp on the p-complete derived category. We give various applications of this approach, including a simplification of the crystalline comparison in AΩ-cohomology theory.