EMS_Algebra_05__Homological_Algebra .pdf

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1、A.I.KostrikinI.R.Shafarevich(Eds.)AlgebraVHomologicalAlgebraMAT000300492'70S.M.1Springer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestEncyclopaediaofMathematicalSciencesVolume38Editor-in-Chief:R.VGamkrelidzeHomologicalAlgebraS.I.Gelfand,Yu.I.ManinCon

2、tentsIntroduction4Chapter1.ComplexesandCohomology8§1.ComplexesandtheExactSequence8§2.StandardComplexesinAlgebraandinGeometry9§3.SpectralSequence17BibliographicHints21Chapter2.TheLanguageofCategories22§1.CategoriesandFunctors22§2.AdditiveandAbelianCategories35§3.FunctorsinAbe

3、lianCategories42§4.ClassicalDerivedFunctors47BibliographicHints52Chapter3.HomologyGroupsinAlgebraandinGeometry52§1.SmallDimensions52§2.Obstructions,Torsors,CharacteristicClasses56§3.Cyclic(Co)Homology60§4.Non-CommutativeDifferentialGeometry67§5.(Co)HomologyofDiscreteGroups71

4、§6.GeneralitiesonLieAlgebraCohomology76§7.ContinuousCohomologyofLieGroups77§8.CohomologyofInfinite-DimensionalLieAlgebras81BibliographicHints852ContentsChapter4.DerivedCategoriesandDerivedFunctors86§1.DefinitionoftheDerivedCategory86§2.DerivedCategoryastheLocalizationofHomot

5、opicCategory92§3.StructureoftheDerivedCategory97§4.DerivedFunctors102§5.SheafCohomology110BibliographicHints120Chapter5.TriangulatedCategories121§1.MainNotions121§2.Examples128§3.Cores133BibliographicHints139Chapter6.MixedHodgeStructures140§0.Introduction140§1.TheCategoryofH

6、odgeStructures142§2.MixedHodgeStructuresonCohomologywithConstantCoefficients145§3.HodgeStructuresonHomotopicInvariants148§4.Hodge-DeligneComplexes153§5.Hodge-DeligneComplexesforSingularandSimplicialVarieties155§6.Hodge-BeilinsonComplexesandDerivedCategoriesofHodgeStructures1

7、57§7.VariationsofHodgeStructures159BibliographicHints162Chapter7.PerverseSheaves163§1.PerverseSheaves163§2.Glueing168BibliographicHints172Chapter8.P-Modules173§0.Introduction173§1.TheWeylAlgebra175§2.AlgebraicP-Modules182§3.InverseImage188§4.DirectImage190§5.HolonomicModules

8、195§6.RegularConnections202Contents3§7.2?-ModuleswithRegularSingularities20