LEADER 03383nam 22004093 450 001 996601572803316 005 20240525060217.0 010 $a3-031-55914-2 035 $a(MiAaPQ)EBC31352504 035 $a(Au-PeEL)EBL31352504 035 $a(CKB)32141991600041 035 $a(EXLCZ)9932141991600041 100 $a20240525d2024 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe P-Adic Simpson Correspondence and Hodge-Tate Local Systems 205 $a1st ed. 210 1$aCham :$cSpringer,$d2024. 210 4$d©2024. 215 $a1 online resource (450 pages) 225 1 $aLecture Notes in Mathematics Series ;$vv.2345 311 $a3-031-55913-4 327 $aIntro -- Preface -- Contents -- Chapter 1 An Overview -- 1.1 Introduction -- 1.2 Faltings Topos -- 1.3 Local Theory. The Torsor of Deformations -- 1.4 Global Theory. Dolbeault Modules -- 1.5 Functoriality of the p-adic Simpson Correspondence by Proper Direct Image -- 1.6 Relative Faltings Topos -- Chapter 2 Preliminaries -- 2.1 Notation and Conventions -- 2.2 Reminder on a Construction by Fontaine-Grothendieck -- 2.3 Fontaine Universal -- -adic Infinitesimal Thickenings -- 2.4 Logarithmic Infinitesimal Thickenings -- 2.5 Higgs Modules and -connections -- 2.6 Ind-objects of a Category -- 2.7 Ind-modules -- 2.8 Higgs Ind-modules and -connections -- 2.9 Modules up to Isogeny -- 2.10 Complement on the Functoriality of Generalized Covanishing Topos -- Chapter 3 The p-adic Simpson Correspondence and Hodge-Tate Modules. Local Study -- 3.1 Assumptions and Notation. -- -adic Infinitesimal Deformations -- 3.2 Torsors and Higgs-Tate Algebras -- 3.3 Dolbeault Representations -- 3.4 Small Higgs Modules -- 3.5 Hodge-Tate Representations -- Chapter 4 The -adic Simpson Correspondence and Hodge-Tate Modules. Global Study -- 4.1 Assumptions and Notation -- 4.2 Higgs Modules -- 4.3 Faltings Topos -- 4.4 Higgs-Tate Algebras in Faltings Topos -- 4.5 Dolbeault ind-modules -- 4.6 Dolbeault Q-modules -- 4.7 Cohomology of Dolbeault ind-modules -- 4.8 Dolbeault Modules Over a Small Affine Scheme -- 4.9 Pullback of a Dolbeault ind-module by an Étale Morphism -- 4.10 Stacky Properties of Dolbeault Modules -- 4.11 Hodge-Tate Modules -- 4.12 Dolbeault and Hodge-Tate Local Systems -- Chapter 5 Relative Cohomologies of Higgs-Tate Algebras. Local Study -- 5.1 Assumptions and Notation. Review of Relative Galois Cohomology -- 5.2 Relative Galois Cohomologies of Higgs-Tate Algebras -- 5.3 Relative Dolbeault Cohomology of Higgs-Tate Algebras. 327 $aChapter 6 Relative Cohomology of Dolbeault Modules -- 6.1 Assumptions and Notation. Relative Faltings Topos -- 6.2 Base Change -- 6.3 Functoriality of Higgs-Tate algebras in Faltings Topos -- 6.4 Cohomological Computations -- 6.5 Relative Cohomology of Dolbeault ind-modules -- Errata and Addenda to "The -adic Simpson Correspondence" -- A) Misprints -- B) Errata -- References -- Index. 410 0$aLecture Notes in Mathematics Series 700 $aAbbes$b Ahmed$0510226 701 $aGros$b Michel$01307890 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996601572803316 996 $aThe P-Adic Simpson Correspondence and Hodge-Tate Local Systems$94165767 997 $aUNISA