D-modules and microlocal calculus / Masaki Kashiwara ; translated by Matsumi Saito.

Format:

Book

Author/Creator:

Kashiwara, Masaki, 1947-

Series:

Translations of mathematical monographs 0065-9282 ; v. 217.

Iwanami series in modern mathematics

Translations of mathematical monographs, 0065-9282 ; v. 217

Standardized Title:

Daisū kaiseki gairon. English

Language:

English

Japanese

Subjects (All):

D-modules.

Microlocal analysis.

Physical Description:

xvi, 254 pages : illustrations ; 22 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2003]

Contents:

1.2. Differential Homomorphisms of O[subscript X]-modules 2

1.3. A System of Generators of D 6

1.4. Left D[subscript X]-modules and Right D[subscript X]-modules 7

Chapter 2. Characteristic Varieties 11

2.1. Cotangent Bundles 11

2.2. Characteristic Varieties 15

2.3. Involutivity 21

2.4. Codimension Filtration 22

Chapter 3. Construction of D-modules 29

3.1. Tensor Products 29

3.2. Homological Properties of D-modules 32

3.3. Dual Module 36

3.4. Algebraic Relative Cohomology 39

Chapter 4. Functorial Properties of D-modules 57

4.1. Pull-backs of D-modules 57

4.2. Derived Functors of Inverse Images 59

4.3. External Tensor Product 60

4.4. Coherence of Inverse Images 61

4.5. Cauchy-Kovalevskaya Theorem 68

4.6. Integrals of D-modules 74

4.7. Coherence of Integrals 76

4.8. D-modules Supported by a Submanifold 84

4.9. Adjunction Formula 87

4.10. Adjunction Formula (Inverse Form) 93

4.11. Holonomic Systems 94

Chapter 5. Regular Holonomic Systems 99

5.1. Ordinary Differential Equations with Regular Singularities 99

5.2. Holonomic Modules with Regular Singularities 100

5.3. Riemann-Hilbert Correspondence 102

Chapter 6. b-functions 105

6.1. Motivation for b-functions 105

6.2. D-module Generated by f(x)[superscript s] 106

6.3. Rationality of b-functions 109

6.4. b-functions in the Case of Quasi-homogeneous Isolated Singularities 114

6.5. b-function and Irreducibility 117

Chapter 7. Ring of Formal Microdifferential Operators 123

7.1. Microlocalization 123

7.2. Formal Microdifferential Operators on Manifolds 125

7.3. Microdifferential Operators 129

7.4. Algebraic Properties of [varepsilon] 130

7.5. Relations between D[subscript X] and [varepsilon subscript X] 139

7.6. Involutivity of the Supports of Coherent [varepsilon]-modules 147

Chapter 8. Microlocal Analysis of Holonomic Systems 153

8.1. Simple [varepsilon]-modules 153

8.2. Quantized Contact Transformation 153

8.3. Subprincipal Symbols 159

8.4. Preparation for the Classification of Simple Holonomic Systems 161

8.5. Classification of Simple Holonomic Systems (1) 168

8.6. Principal Symbols of Simple Holonomic Modules 170

8.7. Regular Holonomic [varepsilon subscript X]-modules 176

8.8. Classification of Simple Holonomic Systems (2) 181

8.9. Subholonomic Systems 186

Chapter 9. Microlocal Calculus of b-functions 191

9.1. Microlocal b-functions 191

9.2. Existence of Microlocal b-functions 196

9.3. Simple Intersection of Lagrangian Analytic Subsets 200

9.4. Relation of b-functions of Two Lagrangian Analytic Subsets with a Good Intersection 201

9.5. b-functions of Relative Invariants 205

A.1. Finiteness of Filtered Rings and Their Modules 213

A.2. Derived Categories 226

A.3. Derived Functors on Categories of Modules 239

A.4. Symplectic Manifolds 243.

Notes:

Includes bibliographical references (pages 247-249) and indexes.

ISBN:

0821827669

OCLC:

50773693