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001 978-3-031-55914-3
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020 _a9783031559143
_9978-3-031-55914-3
024 7 _a10.1007/978-3-031-55914-3
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
100 1 _aAbbes, Ahmed.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_941693
245 1 4 _aThe p-adic Simpson Correspondence and Hodge-Tate Local Systems
_h[electronic resource] /
_cby Ahmed Abbes, Michel Gros.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aX, 443 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2345
505 0 _aPreface -- An overview -- Preliminaries -- Local Study -- Global Study -- Relative cohomologies of Higgs-Tate algebras.Local Study -- Relative cohomology of Dolbeault modules -- References -- Index.
520 _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. .
650 0 _aAlgebraic geometry.
650 1 4 _aAlgebraic Geometry.
700 1 _aGros, Michel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_941694
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031559136
776 0 8 _iPrinted edition:
_z9783031559150
830 0 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2345
_975434
856 4 0 _uhttps://doi.org/10.1007/978-3-031-55914-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-LNM
999 _c59922
_d59922