Gelfand, Manin - Homological Algebra, [Djvu - Eng] [TNTVillage]

Release Originale: [url]http://forum.tntvillage.scambioetico.org/index.php?showtopic=268784[/url]
.:Details:.
Titolo originale: Algebra V: Homological Algebra
Editori: Gelfand, S.I., Manin, Yu.I., Kostrikin, A.I. (ed.), Shafarevich, I.R. (ed.)
Edizione: Springer-Verlag 1994
ISBN: 978-3-540-53373-3
Numero di pagine: 222
Dimensione: 1.4 MB

.:Abstract:. 
    Introduction
    Chapter 1. Complexes and Cohomology
        Complexes and the Exact Sequence
        Standard Complexes in Algebra and in Geometry
        Spectral Sequence
    Chapter 2. The Language of Categories
        Categories and Functors
        Additive and Abelian Categories
        Functors in Abelian Categories
        Classical Derived Functors
    Chapter 3. Homology Groups in Algebra and in Geometry
        Small Dimensions
        Obstructions, Torsors, Characteristic Classes
        Cyclic (Co)Homology
        Non-Commutative Differential Geometry
        (Co)Homology of Discrete Groups
        Generalities on Lie Algebras Cohomology
        Continuous Cohomology of Lie Groups
        Cohomology of Infinite-Dimensional Lie Algebras
    Chapter 4. Derived Categories and Derived Functors
        Definition of the Derived Category
        Derived Category as the Localization of Homotopic Category
        Structure of the Derived Category
        Derived Functors
        Sheaf Cohomology
    Chapter 5. Triangulated Categories
        Main Notions
        Examples
        Cores
    Chapter 6. Mixed Hodge Structures
        Introduction
        The Category of Hodge Structures
        Mixed Hodge Structures on Cohomology with Constant Coefficients
        Hodge Structures on Homotopic Invariants
        Hodge-Deligne Complexes
        Hodge-Deligne Complexes for Singular and Simplicial Varieties
        Hodge-Beilinson Complexes and Derived Categories of Hodge Structures
        Variations of Hodge Structures
    Chapter 7. Perverse Sheaves
        Perverse Sheaves
        Glueing
    Chapter 8. D-Modules
        Introduction
        The Weyl Algebra
        Algebraic D-Modules
        Inverse Image
        Direct Image
        Holonomic Modules
        Regular Connections
        D-Modules with Regular Singularities
        Equivalence of Categories (Riemann-Hilbert Correspondence)
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