Revisiting the de Rham-Witt complex/ Bhargav Bhatt, Jacob Lurie and Akhil Mathew

Includes bibliographical references

Introduction -- Dieudonne complexes -- Dieudonne Algebras -- The Saturated de Rham-Witt complex -- Localizations of Dieudonne algebras -- The case of a Cusp -- Homological algebra -- The Nygaard filtration -- The Derived de Rham-Witt complex -- Comparison with crystalline cohomology -- The Crystalline comparison for AΩ

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>0.
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 for the AΩ-cohomology theory introduced