دانلود کتاب A primer of algebraic D-modules

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Front Cover
TITLE
COPYRIGHT
DEDICATION
CONTENTS
PREFACE
INTRODUCTION
1. THE WEYL ALGEBRA.
2. ALGEBRAIC D-MODULES.
3. THE BOOK: AN OVERVIEW.
4. PRE-REQUISITES .
CHAPTER 1 - THE WEYL ALGEBRA
1. DEFINITION
2. CANONICAL FORM
3. GENERATORS AND RELATIONS
4. EXERCISES
CHAPTER 2 - IDEAL STRUCTURE OF THE WEYL ALGEBRA
1. THE DEGREE OF AN OPERATOR
2. IDEAL STRUCTURE.
3. POSITIVE CHARACTERISTIC.
4. EXERCISES.
CHAPTER 3 - RINGS OF DIFFERENTIAL OPERATORS
1. DEFINITIONS.
2. THE WEYL ALGEBRA.
3. EXERCISES.
CHAPTER 4 - JACOBIAN CONJECTURE
1. POLYNOMIAL MAPS.
2. JACOBIAN CONJECTURE
3. DERIVATIONS
4. AUTOMORPHISMS
5. EXERCISES.
CHAPTER 5 - MODULES OVER THE WEYL ALGEBRA
1. THE POLYNOMIAL RING.
2. TWISTING.
3. HOLOMORPHIC FUNCTIONS.
4. EXERCISES.
CHAPTER 6 - DIFFERENTIAL EQUATIONS
1. THE D-MODULE OF AN EQUATION.
2. DIRECT LIMIT OF MODULES.
3. MICROFUNCTIONS.
4. EXERCISES.
CHAPTER 7 - GRADED AND FILTERED MODULES
1. GRADED RINGS
2. FILTERED RINGS.
3. ASSOCIATED GRADED ALGEBRA.
4. FILTERED MODULES.
5. INDUCED FILTRATIONS.
6. EXERCISES
CHAPTER 8 - NOETHERIAN RINGS AND MODULES
1. NOETHERIAN MODULES.
2. NOETHERIAN RINGS.
3. GOOD FILTRATIONS.
CHAPTER 9 - DIMENSION AND MULTIPLICITY
1. THE HILBERT POLYNOMIAL.
2. DIMENSION AND MULTIPLICITY.
3. BASIC PROPERTIES.
4. BERNSTEIN\'S INEQUALITY.
5. EXERCISES
CHAPTER 10 - HOLONOMIC MODULES
1. DEFINITION AND EXAMPLES.
2. BASIC PROPERTIES.
3. FURTHER EXAMPLES.
4. EXERCISES.
CHAPTER 11 - CHARACTERISTIC VARIETIES
1. THE CHARACTERISTIC VARIETY.
2. SYMPLECTIC GEOMETRY.
3. NON-HOLONOMIC IRREDUCIBLE MODULES
4. EXERCISES
CHAPTER 12 - TENSOR PRODUCTS
1. BIMODULES.
2. TENSOR PRODUCTS.
3. THE UNIVERSAL PROPERTY
4. BASIC PROPERTIES.
5. LOCALIZATION.
6. EXERCISES
CHAPTER 13 - EXTERNAL PRODUCTS
1. EXTERNAL PRODUCTS OF ALGEBRAS.
2. EXTERNAL PRODUCTS OF MODULES.
3. GRADUATIONS AND FILTRATIONS.
4. DIMENSIONS AND MULTIPLICITIES
5. EXERCISES
CHAPTER 14 - INVERSE IMAGES
1. CHANGE OF RINGS
2. INVERSE IMAGES.
3. PROJECTIONS.
4. EXERCISES
CHAPTER 15 - EMBED DINGS
1. THE STANDARD EMBEDDING
2. COMPOSITION.
3. EMBED DINGS REVISITED.
4. EXERCISES
CHAPTER 16 - DIRECT IMAGES
1. RIGHT MODULES
2. TRANSPOSITION
3. LEFT MODULES
4. EXERCISES
CHAPTER 17 - KASHIWARA\'S THEOREM
1. EMBEDDINGS
2. KASHIWARA\'S THEOREM
3. EXERCISES
CHAPTER 18 - PRESERVATION OF HOLONOMY
1. INVERSE IMAGES
2. DIRECT IMAGES.
3. CATEGORIES AND FUNCTORS.
4. EXERCISES
CHAPTER 19 - STABILITY OF DIFFERENTIAL EQUATIONS
1. ASYMPTOTIC STABILITY
2. GLOBAL UPPER BOUND
3. GLOBAL STABILITY ON THE PLANE
4. EXERCISES
CHAPTER 20 - AUTOMATIC PROOF OF IDENTITIES
1. HOLONOMIC FUNCTIONS.
2. HYPEREXPONENTIAL FUNCTIONS.
3. THE METHOD.
4. EXERCISES
CODA
APPENDIX 1 - DEFINING THE ACTION OF A MODULE USING GENERATORS
APPENDIX 2 - LOCAL INVERSION THEOREM
REFERENCES
INDEX
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