LEADER 06228nam 2201369 450 001 9910797970703321 005 20210506031702.0 010 $a1-4008-8123-4 024 7 $a10.1515/9781400881239 035 $a(CKB)3710000000553943 035 $a(EBL)4198328 035 $a(OCoLC)934626614 035 $a(SSID)ssj0001593815 035 $a(PQKBManifestationID)16287713 035 $a(PQKBTitleCode)TC0001593815 035 $a(PQKBWorkID)14290349 035 $a(PQKB)10451754 035 $a(MiAaPQ)EBC4198328 035 $a(StDuBDS)EDZ0001756491 035 $a(DE-B1597)468646 035 $a(OCoLC)979882297 035 $a(DE-B1597)9781400881239 035 $a(Au-PeEL)EBL4198328 035 $a(CaPaEBR)ebr11140062 035 $a(CaONFJC)MIL887637 035 $a(PPN)201991365 035 $a(EXLCZ)993710000000553943 100 $a20150903d2016 uy| 0 101 0 $aeng 135 $aurnnu---|u||u 181 $ctxt 182 $cc 183 $acr 200 14$aThe p-adic Simpson correspondence /$fAhmed Abbes, Michel Gros, Takeshi Tsuji 210 1$aPrinceton, New Jersey :$cPrinceton University Press,$d2016. 215 $a1 online resource (618 p.) 225 1 $aAnnals of mathematics studies ;$vnumber 193 300 $aDescription based upon print version of record. 311 0 $a0-691-17029-0 311 0 $a0-691-17028-2 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tForeword --$tChapter I. Representations of the fundamental group and the torsor of deformations. An overview /$rAbbes, Ahmed / Gros, Michel --$tChapter II. Representations of the fundamental group and the torsor of deformations. Local study /$rAbbes, Ahmed / Gros, Michel --$tChapter III. Representations of the fundamental group and the torsor of deformations. Global aspects /$rAbbes, Ahmed / Gros, Michel --$tChapter IV. Cohomology of Higgs isocrystals /$rTsuji, Takeshi --$tChapter V. Almost étale coverings /$rTsuji, Takeshi --$tChapter VI. Covanishing topos and generalizations /$rAbbes, Ahmed / Gros, Michel --$tFacsimile : A p-adic Simpson correspondence /$rFaltings, Gerd --$tBibliography --$tIndexes 330 $aThe p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra-namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation.The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos. 410 0$aAnnals of mathematics studies ;$vno. 193. 606 $aGroup theory 606 $ap-adic groups 606 $aGeometry, Algebraic 610 $aDolbeault generalized representation. 610 $aDolbeault module. 610 $aDolbeault representation. 610 $aFaltings cohomology. 610 $aFaltings extension. 610 $aFaltings ringed topos. 610 $aFaltings site. 610 $aFaltings topos. 610 $aGalois cohomology. 610 $aGerd Faltings. 610 $aHiggs bundle. 610 $aHiggs bundles. 610 $aHiggs crystals. 610 $aHiggs envelopes. 610 $aHiggs isocrystal. 610 $aHiggs?ate algebra. 610 $aHodge?ate representation. 610 $aHodge?ate structure. 610 $aHodge?ate theory. 610 $aHyodo's theory. 610 $aKoszul complex. 610 $aadditive categories. 610 $aadic module. 610 $aalmost faithfully flat descent. 610 $aalmost faithfully flat module. 610 $aalmost flat module. 610 $aalmost isomorphism. 610 $aalmost tale covering. 610 $aalmost tale extension. 610 $acohomology. 610 $acovanishing topos. 610 $acrystalline-type topos. 610 $adeformation. 610 $adiscrete A?-module. 610 $afinite tale site. 610 $afundamental group. 610 $ageneralized covanishing topos. 610 $ageneralized representation. 610 $ainverse limit. 610 $alinear algebra. 610 $alocally irreducible scheme. 610 $amorphism. 610 $aoverconvergence. 610 $ap-adic Hodge theory. 610 $ap-adic Simpson correspondence. 610 $ap-adic field. 610 $aperiod ring. 610 $aringed covanishing topos. 610 $aringed total topos. 610 $asmall generalized representation. 610 $asmall representation. 610 $asolvable Higgs module. 610 $atale cohomology. 610 $atale fundamental group. 610 $atorsor. 615 0$aGroup theory. 615 0$ap-adic groups. 615 0$aGeometry, Algebraic. 676 $a512/.2 686 $aSI 830$2rvk 700 $aAbbes$b Ahmed$0510226 702 $aGros$b Michel$f1956- 702 $aTsuji$b Takeshi$f1967- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910797970703321 996 $aThe p-adic Simpson correspondence$93774825 997 $aUNINA