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

Format:

Book

Author/Creator:

Bhatt, Bhargav, 1983- author.

Lurie, Jacob, 1977- author.

Mathew, Akhil, author.

Series:

Astérisque ; 0303-1179 424.

Astérisque, 0303-1179 ; numéro 424, 2021

Language:

English

French

Subjects (All):

Homology theory.

Algebraic varieties.

Geometry, Algebraic.

Physical Description:

viii, 165 pages ; 24 cm.

Place of Publication:

Paris, France : Société mathématique de France, 2021.

Language Note:

Text in English with English and French abstracts.

Summary:

The goal of this book is to offer a new construction of the de Rham-Witt complex of a smooth variety over a perfect field of characteristic p> 0. We introduce a category of cochain complexes which are 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 in [12].

Notes:

Includes bibliographical references (pages 161-165).

Current Copyright Fee: GBP22.50 0.

ISBN:

9782856299371

2856299377

OCLC:

1260249804

Publisher Number:

10.24033/ast.1146