The p-adic Simpson correspondence and Hodge-Tate local systems

Preface -- An overview -- Preliminaries -- Local Study -- Global Study -- Relative cohomologies of Higgs-Tate algebras.Local Study -- Relative cohomology of Dolbeault modules -- References -- Index.

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Hauptverfasser: Abbes, Ahmed 1970- (VerfasserIn), Gros, Michel 1956- (VerfasserIn)
Format: Buch
Sprache:English
Veröffentlicht: Cham, Switzerland Springer [2024]
Schriftenreihe:Lecture notes in mathematics Volume 2345
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Datensatz im Suchindex

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spelling Abbes, Ahmed 1970- (DE-588)1090806434 aut
The p-adic Simpson correspondence and Hodge-Tate local systems Ahmed Abbes ; Michel Gros
Cham, Switzerland Springer [2024]
© 2024
x, 443 Seiten
txt rdacontent
n rdamedia
nc rdacarrier
Lecture notes in mathematics Volume 2345
Preface -- An overview -- Preliminaries -- Local Study -- Global Study -- Relative cohomologies of Higgs-Tate algebras.Local Study -- Relative cohomology of Dolbeault modules -- References -- Index.
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. .
Geometry, Algebraic
Group theory
p-adic groups
Algebraic geometry
Gros, Michel 1956- (DE-588)1090896387 aut
Erscheint auch als Online-Ausgabe 978-3-031-55914-3
Lecture notes in mathematics Volume 2345 (DE-604)BV000676446 2345
spellingShingle Abbes, Ahmed 1970-
Gros, Michel 1956-
The p-adic Simpson correspondence and Hodge-Tate local systems
Lecture notes in mathematics
Geometry, Algebraic
Group theory
p-adic groups
title The p-adic Simpson correspondence and Hodge-Tate local systems
title_auth The p-adic Simpson correspondence and Hodge-Tate local systems
title_exact_search The p-adic Simpson correspondence and Hodge-Tate local systems
title_full The p-adic Simpson correspondence and Hodge-Tate local systems Ahmed Abbes ; Michel Gros
title_fullStr The p-adic Simpson correspondence and Hodge-Tate local systems Ahmed Abbes ; Michel Gros
title_full_unstemmed The p-adic Simpson correspondence and Hodge-Tate local systems Ahmed Abbes ; Michel Gros
title_short The p-adic Simpson correspondence and Hodge-Tate local systems
title_sort the p adic simpson correspondence and hodge tate local systems
topic Geometry, Algebraic
Group theory
p-adic groups
topic_facet Geometry, Algebraic
Group theory
p-adic groups
volume_link (DE-604)BV000676446
work_keys_str_mv AT abbesahmed thepadicsimpsoncorrespondenceandhodgetatelocalsystems
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