06228nam 2201369 450 991079797070332120210506031702.01-4008-8123-410.1515/9781400881239(CKB)3710000000553943(EBL)4198328(OCoLC)934626614(SSID)ssj0001593815(PQKBManifestationID)16287713(PQKBTitleCode)TC0001593815(PQKBWorkID)14290349(PQKB)10451754(MiAaPQ)EBC4198328(StDuBDS)EDZ0001756491(DE-B1597)468646(OCoLC)979882297(DE-B1597)9781400881239(Au-PeEL)EBL4198328(CaPaEBR)ebr11140062(CaONFJC)MIL887637(PPN)201991365(EXLCZ)99371000000055394320150903d2016 uy| 0engurnnu---|u||utxtccrThe p-adic Simpson correspondence /Ahmed Abbes, Michel Gros, Takeshi TsujiPrinceton, New Jersey :Princeton University Press,2016.1 online resource (618 p.)Annals of mathematics studies ;number 193Description based upon print version of record.0-691-17029-0 0-691-17028-2 Includes bibliographical references and index.Front matter --Contents --Foreword --Chapter I. Representations of the fundamental group and the torsor of deformations. An overview /Abbes, Ahmed / Gros, Michel --Chapter II. Representations of the fundamental group and the torsor of deformations. Local study /Abbes, Ahmed / Gros, Michel --Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects /Abbes, Ahmed / Gros, Michel --Chapter IV. Cohomology of Higgs isocrystals /Tsuji, Takeshi --Chapter V. Almost étale coverings /Tsuji, Takeshi --Chapter VI. Covanishing topos and generalizations /Abbes, Ahmed / Gros, Michel --Facsimile : A p-adic Simpson correspondence /Faltings, Gerd --Bibliography --IndexesThe p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra-namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation.The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos.Annals of mathematics studies ;no. 193.Group theoryp-adic groupsGeometry, AlgebraicDolbeault generalized representation.Dolbeault module.Dolbeault representation.Faltings cohomology.Faltings extension.Faltings ringed topos.Faltings site.Faltings topos.Galois cohomology.Gerd Faltings.Higgs bundle.Higgs bundles.Higgs crystals.Higgs envelopes.Higgs isocrystal.HiggsДate algebra.HodgeДate representation.HodgeДate structure.HodgeДate theory.Hyodo's theory.Koszul complex.additive categories.adic module.almost faithfully flat descent.almost faithfully flat module.almost flat module.almost isomorphism.almost tale covering.almost tale extension.cohomology.covanishing topos.crystalline-type topos.deformation.discrete AЇ-module.finite tale site.fundamental group.generalized covanishing topos.generalized representation.inverse limit.linear algebra.locally irreducible scheme.morphism.overconvergence.p-adic Hodge theory.p-adic Simpson correspondence.p-adic field.period ring.ringed covanishing topos.ringed total topos.small generalized representation.small representation.solvable Higgs module.tale cohomology.tale fundamental group.torsor.Group theory.p-adic groups.Geometry, Algebraic.512/.2SI 830rvkAbbes Ahmed510226Gros Michel1956-Tsuji Takeshi1967-MiAaPQMiAaPQMiAaPQBOOK9910797970703321The p-adic Simpson correspondence3774825UNINA