The P-Adic Simpson Correspondence and Hodge-Tate Local Systems

• Record Nr.: UNISA996601572803316
• Autore: Abbes Ahmed
• Pubbl/distr/stampa: Cham : , : Springer, , 2024; ©2024
• ISBN: 3-031-55914-2
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (450 pages)
• Collana: Lecture Notes in Mathematics Series ; ; v.2345
• Altri autori (Persone): GrosMichel
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- 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.; Chapter 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.