The p-adic Simpson correspondence and Hodge-Tate local systems / Ahmed Abbes, Michel Gros.

Format:

Book

Author/Creator:

Abbes, Ahmed, author.

Contributor:

Gros, Michel, 1956-

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2345.

Lecture notes in mathematics, 0075-8434 ; volume 2345

Language:

English

Subjects (All):

p-adic groups.

Hodge theory.

Geometry, Algebraic.

Physical Description:

x, 443 pages ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2024]

Summary:

This book delves into the p-adic Simpson correspondence, its construction, and development. Offering fresh and innovative perspectives on this important topic in algebraic geometry, the text serves a dual purpose: it describes an important tool in p-adic Hodge theory, which has recently attracted significant interest, and also provides a comprehensive resource for researchers. Unique among the books in the existing literature in this field, it combines theoretical advances, novel constructions, and connections to Hodge-Tate local systems. This exposition builds upon the foundation laid by Faltings, the collaborative efforts of the two authors with T. Tsuji, and contributions from other researchers. Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson correspondence, whose construction has been taken up in several different ways. Following the approach they initiated with T. Tsuji, the authors develop new features of the p-adic Simpson correspondence, inspired by their construction of the relative Hodge-Tate spectral sequence. First, they address the connection to Hodge-Tate local systems. Then they establish the functoriality of the p-adic Simpson correspondence by proper direct image. Along the way, they expand the scope of their original construction. The book targets a specialist audience interested in the intricate world of p-adic Hodge theory and its applications, algebraic geometry and related areas. Graduate students can use it as a reference or for in-depth study. Mathematicians exploring connections between complex and p-adic geometry will also find it valuable. .

Contents:

Preface

An overview

Preliminaries

Local Study

Global Study

Relative cohomologies of Higgs-Tate algebras.Local Study

Relative cohomology of Dolbeault modules

References

Index.

Notes:

Includes bibliographical references (pages 433-435) and index.

ISBN:

9783031559136

3031559134

OCLC:

1439147309