Homology of Analytic Sheaves and Duality Theorems

Inhaltsverzeichnis

• 1. Analytic Sheaves.
• 1. Preliminary Information.
• 2. Injectivity Test.
• 3. Local Duality.
• 4. Injective and Global Dimension.
• 5. Properties of Fine Sheaves.
• 2. Homology Theory.
• 1. Sheaves of Germs of Homology.
• 2. Homology Groups.
• 3. Connection with the Functors Ext.
• 4. Poincaré Duality.
• 5. Dualizing Complexes.
• 3. Duality Theorems.
• 1. Homology of Coverings.
• 2. Cohomology with Arbitrary Supports.
• 3. Cohomology with Compact Supports.
• 4. Holomorphically Complete Spaces.
• 5. Leray Spectral Sequence.
• 4. Local Homology.
• 1. Homology of a Closed Set.
• 2. Local Homology.
• 4. Inductive and Projective Limits.
• 5. Tests for Separatedness.
• 5. Applications.
• 1. Dimension of Support.
• 2. Homological Codimension.
• 3. The Results of Andreotti—Grauert.
• 4. Lefschetz Theorem.
• 5. Theory of Hyperfunctions.
• Notes.
• References.