Regular and irregular holonomic D-modules:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, United Kingdom
Cambridge University Press
2016
|
| Series: | London Mathematical Society lecture note series
433 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | vi, 111 Seiten |
| ISBN: | 9781316613450 |
Staff View
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| 245 | 1 | 0 | |a Regular and irregular holonomic D-modules |c Masaki Kashiwara (Research Institute for Mathematical Sciences, Kyoto University), Pierre Schapira (Pierre and Marie Curie University, Paris) |
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Record in the Search Index
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| adam_text | Contents
Introduction page 1
X A review on sheaves and D-modules 7
1.1 Sheaves 7
1.2 D-modules 9
2 Indsheaves 18
2.1 Ind-objects 18
2.2 Indsheaves 20
2.3 Ring action 23
2.4 Sheaves on the subanalytic site 26
2.5 Some classical sheaves on the subanalytic site 29
3 Tempered solutions of D-modules 39
3.1 Tempered de Rham and Sol functors 39
3.2 Localization along a hypersurface 42
4 Regular holonomie D-modules 44
4.1 Regular normal form for holonomie modules 44
4.2 Real blow up 48
4.3 Regular Riemann-Hilbert correspondence 51
4.4 Integral transforms with regular kernels 55
4.5 Irregular D-modules: an example 56
5 Indsheaves on bordered spaces 58
5.1 Bordered spaces 58
5.2 Operations 60
6 Enhanced indsheaves 63
6.1 Tamarkin’s construction 63
6.2 Convolution products 64
v
Contents
vi
6.3 Enhanced indsheaves 67
6.4 Operations on enhanced indsheaves 69
6.5 Stable objects 72
6.6 Constructible enhanced indsheaves 74
6.7 Enhanced indsheaves with ring action 77
7 Holonomie D-modules 79
7.1 Exponential D-modules 79
7.2 Enhanced tempered holomorphie functions 80
7.3 Enhanced de Rham and Sol functors 81
7.4 Ordinary linear differential equations and Stokes phenomena 82
7.5 Normal form 86
7.6 Enhanced de Rham functor on the real blow up 88
7.7 De Rham functor: constructibility and duality 89
7.8 Enhanced Riemann-Hilbert correspondence 94
8 Integral transforms 97
8.1 Integral transforms with irregular kernels 97
8.2 Enhanced Fourier—Sato transform 98
8.3 Laplace transform 100
References 104
Notations 107
Index 110
LONDON MATHEMATICAL SOCIETY
LECTURE NOTE SERIES
Edited by P K o ï; essor M. R v. i r
Mathematics Institute, University of Warwick,
Uniteti Kingdom
Coventry CV4 7AL
with the assistance of
B. J. Green (Cambridge)
D. R. Heath-Brown (Oxford)
R. A. M. Rouquicr (Oxford)
J, T. Stafford (Manchester)
E. Siili (Oxford)
The London Mathematical Society is incorporated under Royal Charter.
Regular and irregular Holonomie D-Modules
Masaki Kashiwara and Pierre Schapira
D-module theory is essentially the algebraic study of systems ofi inear
partial differential equations. This book., the first devoted specifically to
holonomie D-modules, provides a unified treatment of both régula rand
irregular D-modules.
The authors begin by recalling the main results of the theory of indsheave
and suhanalytic sheaves, explaining in detail the operations on D-modules
and their tempered holomorphic solutions. As an application, they obtain
the Riemaruv-Hilbert correspondence for regular holonomie D-modulcs.
In the second part of the book the authors do the same for the sheaf of
enhanced tempered solutions of (not necessarily regular) holonomie
D-modulcs.
Originating from a scries of lectures given at the Institut des Hautes
Études Scientifiques, this book is addressed to graduate students and
researchers familiar with the language of sheaves and D-modules, in the
derived sense.
|
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| id | DE-604.BV043587701 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:30:20Z |
| institution | BVB |
| isbn | 9781316613450 |
| language | English |
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| physical | vi, 111 Seiten |
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| publisher | Cambridge University Press |
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| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Kashiwara, Masaki 1947- Verfasser (DE-588)122204344 aut Regular and irregular holonomic D-modules Masaki Kashiwara (Research Institute for Mathematical Sciences, Kyoto University), Pierre Schapira (Pierre and Marie Curie University, Paris) Cambridge, United Kingdom Cambridge University Press 2016 vi, 111 Seiten txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 433 D-Modul (DE-588)4305548-5 gnd rswk-swf D-Modul (DE-588)4305548-5 s DE-604 Schapira, Pierre 1943- Verfasser (DE-588)10785130X aut London Mathematical Society lecture note series 433 (DE-604)BV000000130 433 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029002205&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029002205&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kashiwara, Masaki 1947- Schapira, Pierre 1943- Regular and irregular holonomic D-modules London Mathematical Society lecture note series D-Modul (DE-588)4305548-5 gnd |
| subject_GND | (DE-588)4305548-5 |
| title | Regular and irregular holonomic D-modules |
| title_auth | Regular and irregular holonomic D-modules |
| title_exact_search | Regular and irregular holonomic D-modules |
| title_full | Regular and irregular holonomic D-modules Masaki Kashiwara (Research Institute for Mathematical Sciences, Kyoto University), Pierre Schapira (Pierre and Marie Curie University, Paris) |
| title_fullStr | Regular and irregular holonomic D-modules Masaki Kashiwara (Research Institute for Mathematical Sciences, Kyoto University), Pierre Schapira (Pierre and Marie Curie University, Paris) |
| title_full_unstemmed | Regular and irregular holonomic D-modules Masaki Kashiwara (Research Institute for Mathematical Sciences, Kyoto University), Pierre Schapira (Pierre and Marie Curie University, Paris) |
| title_short | Regular and irregular holonomic D-modules |
| title_sort | regular and irregular holonomic d modules |
| topic | D-Modul (DE-588)4305548-5 gnd |
| topic_facet | D-Modul |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029002205&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029002205&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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