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

By: Contributor(s): Material type: TextTextSeries: Asterisque ; 424Publication details: Paris: Societe mathematique De France, 2021Description: viii,168 pages, 23 cmISBN:
  • 9782856299371
Subject(s): DDC classification:
  • 23 512 As853
Contents:
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
Summary: 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
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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

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