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Gelfand, Manin - Homological Algebra, [Djvu - Eng] [TNTVillage]
Release Originale: http://forum.tntvillage.scambioetico.org/index.php?showtopic=268784
.: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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