03292nam a22004095i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184072001600207100007500223245012200298250001800420264006900438300003200507336002600539337002600565338003600591347002400627490005300651505020300704520162100907650002402528650002402552700007502576710003402651773002602685776003602711776003602747830005302783856004602836978-3-031-55914-3DE-He21320251030112046.0cr nn 008mamaa240523s2024    sz |    s    |||| 0|eng d  a97830315591437 a10.1007/978-3-031-55914-32doi 4aQA564-609 7aPBMW2bicssc 7aMAT0120102bisacsh 7aPBMW2thema1 aAbbes, Ahmed.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut14aThe p-adic Simpson Correspondence and Hodge-Tate Local Systemsh[electronic resource] /cby Ahmed Abbes, Michel Gros.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aX, 443 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLecture Notes in Mathematics,x1617-9692 ;v23450 aPreface -- An overview -- Preliminaries -- Local Study -- Global Study -- Relative cohomologies of Higgs-Tate algebras.Local Study -- Relative cohomology of Dolbeault modules -- References -- Index.  aThis 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. . 0aAlgebraic geometry.14aAlgebraic Geometry.1 aGros, Michel.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303155913608iPrinted edition:z9783031559150 0aLecture Notes in Mathematics,x1617-9692 ;v234540uhttps://doi.org/10.1007/978-3-031-55914-3