A primer of algebraic D-modules:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2003
|
| Ausgabe: | transferred to digital print. |
| Schriftenreihe: | London Mathematical Society student texts
33 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 207 S. |
| ISBN: | 0521551196 0521559081 |
Internformat
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| 245 | 1 | 0 | |a A primer of algebraic D-modules |c S. C. Coutinho |
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| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2003 | |
| 300 | |a XII, 207 S. | ||
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| 490 | 1 | |a London Mathematical Society student texts |v 33 | |
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| 650 | 7 | |a D-module |2 inriac | |
| 650 | 7 | |a D-modules, Théorie des |2 ram | |
| 650 | 7 | |a algèbre Weyl |2 inriac | |
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| 650 | 7 | |a module algébrique |2 inriac | |
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Datensatz im Suchindex
| _version_ | 1804128879845048320 |
|---|---|
| adam_text | CONTENTS
Preface xi
Introduction
1. The Weyl algebra 1
2. Algebraic .D modules 3
3. The book: an overview 5
4. Pre requisites 6
Chapter 1. The Weyl algebra
1. Definition 8
2. Canonical form 9
3. Generators and relations 10
4. Exercises 12
Chapter 2. Ideal structure of the Weyl algebra.
1. The degree of an operator 14
2. Ideal structure 16
3. Positive characteristic 17
4. Exercises 18
Chapter 3. Rings of differential operators.
1. Definitions 20
2. The Weyl algebra 22
3. Exercises 24
Chapter 4. Jacobian Conjecture.
1. Polynomial maps 26
2. Jacobian conjecture 28
3. Derivations 30
4. Automorphisms 32
5. Exercises 34
Chapter 5. Modules over the Weyl algebra.
1. The polynomial ring 36
2. Twisting 38
3. Holomorphic functions 40
4. Exercises 41
viii Contents
Chapter 6. Differential equations.
1. The D module of an equation 44
2. Direct limit of modules 46
3. Microfunctions 48
4. Exercises 50
Chapter 7. Graded and filtered modules.
1. Graded rings 53
2. Filtered rings 55
3. Associated graded algebra 57
4. Filtered modules 59
5. Induced filtration 60
6. Exercises 62
Chapter 8. Noetherian rings and modules.
1. Noetherian modules 65
2. Noetherian rings 67
3. Good filtrations 70
4. Exercises 72
Chapter 9. Dimension and multiplicity.
1. The Hilbert polynomial 74
2. Dimension and multiplicity 77
3. Basic properties 80
4. Bernstein s inequality 82
5. Exercises 84
Chapter 10. Holonomic modules.
1. Definition and examples 86
2. Basic properties 88
3. Further examples 91
4. Exercises 95
Chapter 11. Characteristic varieties.
1. The characteristic variety 97
2. Symplectic geometry 100
3. Non holonomic irreducible modules 104
4. Exercises 106
Chapter 12. Tensor products.
1. Bimodules 108
2. Tensor products 109
3. The universal property 111
Contents ix
4. Basic properties 113
5. Localization 117
6. Exercises 119
Chapter 13. External products.
1. External products of algebras 121
2. External products of modules 122
3. Graduations and filtrations 124
4. Dimensions and multiplicities 127
5. Exercises 128
Chapter 14. Inverse Image.
1. Change of rings 130
2. Inverse images 132
3. Projections 134
4. Exercises 135
Chapter 15. Embeddings.
1. The standard embedding 138
2. Composition 139
3. Embeddings revisited 142
4. Exercises 144
Chapter 16. Direct images.
1. Right modules 146
2. Transposition 147
3. Left modules 150
4. Exercises 153
Chapter 17. Kashiwara s theorem.
1. Embeddings 154
2. Kashiwara s theorem 156
3. Exercises 160
Chapter 18. Preservation of holonomy.
1. Inverse images 162
2. Direct images 165
3. Categories and functors 166
4. Exercises 170
Chapter 19. Stability of differential equations.
1. Asymptotic stability 171
2. Global upper bound 173
3. Global stability on the plane 176
4. Exercises 178
x Contents
Chapter 20. Automatic proof of identities.
1. Holonomic functions 179
2. Hyperexponential functions 180
3. The method 183
4. Exercises 186
Coda 188
Appendix 1. Defining the action of a module using generators 191
Appendix 2. Local inversion theorem 194
References 197
Index 203
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | transferred to digital print. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:56:16Z |
| institution | BVB |
| isbn | 0521551196 0521559081 |
| language | English |
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| physical | XII, 207 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge Univ. Press |
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| series | London Mathematical Society student texts |
| series2 | London Mathematical Society student texts |
| spelling | Coutinho, Severino Collier Verfasser aut A primer of algebraic D-modules S. C. Coutinho transferred to digital print. Cambridge Cambridge Univ. Press 2003 XII, 207 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 33 Anneaux (algèbre) ram D-module inriac D-modules, Théorie des ram algèbre Weyl inriac anneau associatif inriac module algébrique inriac opérateur différentiel inriac équation différentielle inriac D-modules Weyl-Algebra (DE-588)4373964-7 gnd rswk-swf D-Modul (DE-588)4305548-5 gnd rswk-swf D-Modul (DE-588)4305548-5 s Weyl-Algebra (DE-588)4373964-7 s DE-604 London Mathematical Society student texts 33 (DE-604)BV000841726 33 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009600722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Coutinho, Severino Collier A primer of algebraic D-modules London Mathematical Society student texts Anneaux (algèbre) ram D-module inriac D-modules, Théorie des ram algèbre Weyl inriac anneau associatif inriac module algébrique inriac opérateur différentiel inriac équation différentielle inriac D-modules Weyl-Algebra (DE-588)4373964-7 gnd D-Modul (DE-588)4305548-5 gnd |
| subject_GND | (DE-588)4373964-7 (DE-588)4305548-5 |
| title | A primer of algebraic D-modules |
| title_auth | A primer of algebraic D-modules |
| title_exact_search | A primer of algebraic D-modules |
| title_full | A primer of algebraic D-modules S. C. Coutinho |
| title_fullStr | A primer of algebraic D-modules S. C. Coutinho |
| title_full_unstemmed | A primer of algebraic D-modules S. C. Coutinho |
| title_short | A primer of algebraic D-modules |
| title_sort | a primer of algebraic d modules |
| topic | Anneaux (algèbre) ram D-module inriac D-modules, Théorie des ram algèbre Weyl inriac anneau associatif inriac module algébrique inriac opérateur différentiel inriac équation différentielle inriac D-modules Weyl-Algebra (DE-588)4373964-7 gnd D-Modul (DE-588)4305548-5 gnd |
| topic_facet | Anneaux (algèbre) D-module D-modules, Théorie des algèbre Weyl anneau associatif module algébrique opérateur différentiel équation différentielle D-modules Weyl-Algebra D-Modul |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009600722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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