流形上的层

Introduction

A Short History: Les Debuts De La Theorie des Faheeaux By Christian Houzel

1. Homologieal Algebra

Summary

1.1. Categories and Functors

1.2. Abelian Categories

1.3. Categories of Complexes

1.4. Mapping Cones

1.5. Triangulated Categories

1.6. Localization of Categories

1.7. Derived Categories

1.8. Derived Functors

1.9. Double Complexes

1.10. Bifunctors

1.11. Ind-Objects And Pro-Objects

1.12. The Mittag-Leffler Condition

Exercises To Chapter I

Notes

Ⅱ.Sheaves

Summary

2.1. Presheaves

2.2. Sheaves

2.3. Operations on Sheaves

2.4. Injective, Flabby and Flat Sheaves

2.5. Sheaves on Locally Compact Spaces

2.6. Cohomology of Sheaves

2.7. Some Vanishing Theorems

2.8. Cohomology of Coverings

2.9. Examples of Sheaves on Real and Complex Manifolds

……

Ⅲ. poincare. verdier duality and fourier-sato transformation

Ⅳ. specialization and microlocalization

Ⅴ. micro-support of sheaves

Ⅵ. micro-support and microlocalization

Ⅶ. contact transformations and pure sheaves

Ⅷ. constructible sheaves

Ⅸ. characteristic cycles

Ⅹ. perverse sheaves

Ⅺ. applications to θ-modules and d-modules

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