03656nam a22005055i 4500 978-3-031-55914-3 DE-He213 20251030112046.0 cr nn 008mamaa 240523s2024 sz | s |||| 0|eng d 9783031559143 978-3-031-55914-3 10.1007/978-3-031-55914-3 doi QA564-609 PBMW bicssc MAT012010 bisacsh PBMW thema Abbes, Ahmed. author. aut http://id.loc.gov/vocabulary/relators/aut 41693 The p-adic Simpson Correspondence and Hodge-Tate Local Systems [electronic resource] / by Ahmed Abbes, Michel Gros. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. X, 443 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Mathematics, 1617-9692 ; 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. . Algebraic geometry. Algebraic Geometry. Gros, Michel. author. aut http://id.loc.gov/vocabulary/relators/aut 41694 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031559136 Printed edition: 9783031559150 Lecture Notes in Mathematics, 1617-9692 ; 2345 75434 https://doi.org/10.1007/978-3-031-55914-3 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM 59922 59922