Analytic D-Modules and Applications

Inhaltsverzeichnis

• I. The sheaf DX and its modules.
• II. Operations on D-modules.
• III. Holonomic D-modules.
• IV. Deligne modules.
• V. Regular holonomic D-modules.
• VI. b-functions.
• VII. Distributions and regular holonomic systems.
• VIII. Microdifferential operators.
• A: I Derived Categories.
• Summary.
• A: I.1 The construction of derived categories.
• A: I.2. Properties of derived categories.
• A: I.3. Injective resolutions.
• A: I.4. Spectral sequences.
• A: II Sheaf Theory.
• A: II.1. The category of sheaves.
• A: II.2. Operations on sheaves.
• A: II.3. The derived category of sheaves.
• A: II.4. Flabby sheaves.
• A: II.5. Sheaves on paracompact manifolds.
• A: II.6. Ringed spaces.
• A: II.7. Derived categories of modules.
• A: III Filtered rings.
• A: III.1. Filtered rings.
• A: III.2. Filtered sheaves of rings.
• A: III.3. Gabber’s Theorem.
• A: IV Homological algebra.
• A: IV.1. Basic facts in homological algebra.
• A: IV.2. Auslander regular rings.
• A: IV.3. Commutative algebra.
• A: IV.4. Filtered Auslander regular rings.
• A: V Complex analysis.
• A: V.2. Analysis on complex manifolds.
• A: V.4. The local Milnor fibrations.
• A: VI Analytic geometry.
• A: VI.1. Subanalytic sets.
• A: VII Symplectic analysis.
• A: VII.1. Symplectic algebra.
• A: VII:3. Lagrangian varieties.
• A: VII.4. Lagrangian varieties in generic position.
• References.
• List of notations.