Introduction Chapter1.Homological Machinery 1.Origins of Homological Concepts 1.1 the Idea of Homology 1.2 Homology of Triangulated Spaces 1.3 Singular Homology 1.4 Cohomology 1.5 Sheaves 1.6 Cohomology of Shaves 1.7 Cohomology of Coherent Sheaves 1.8 Cohomology of Etale Sheaves 2 Complexes 2.1 Exact Sequences 2.2 Complexes 2.3 A Long Exact Sequence 2.4 Filtred Complexes 2.5 Spectral Sequences 2.6 Bicomplexes 2.7 Mapping Cone 2.8 Products 3.Sheaves 3.1 Presheaves 3.2 Sheaves 3.3 Direct and Inverse Images of Sheaves 3.4 Abelian Sheaves 3.5 Flabby Sheaves 4.Cohomology of Sheaves 4.1 Construction of Cohomology 4.2 Hypercohomology 4.3 Higher Direct Images 4.4 The Acyclicity Criterion for Coverings Chapter2.Cohomology of Coherent Sheaves 1.Cohomology of Quasi-Coherint Sheaves 2.Cohomology of Projective Space 3.Cohomology of Proper Morphisms 4.The Riemann-Roch Theorem 5.Duality 6.The de Rham Cohology Chapter3.Cohomology of Complex Varieties 1.Complex Varieties as Topological Spaces 2.Cohomology of Coherent Sheaves 3.Weights in Cohomology 4.Algebraic Approach to Classical Topolpgy Chapter4.Etale Cohomology 1.The Weil Conjectures 2.Algebraic Fundamental Group 3.Etale Topology 4.Cohomology of Etale Sheaves 5.Cohomology of Algebraic Curves 6.Fundamental Theorems 7.l-Adic Cohomology 8.Deligne's Theorem Bibliography References
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