Introduction to Stokes structures:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Lecture notes in mathematics
2060 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIV, 249 S. Ill., graph. Darst. 235 mm x 155 mm |
| ISBN: | 3642316948 9783642316944 |
Internformat
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| 245 | 1 | 0 | |a Introduction to Stokes structures |c Claude Sabbah |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XIV, 249 S. |b Ill., graph. Darst. |c 235 mm x 155 mm | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 2060 | |
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
INTRODUCTION IX
1 J-FILTRATIONS 1
1.1 INTRODUCTION 1
1.2 ETALE SPACES OF SHEAVES 2
1.3 ETALE SPACES OF SHEAVES OF ORDERED ABELIAN GROUPS 3
1.4 THE CATEGORY OF PRE-3-FILTRATIONS 5
1.5 TRACES FOR ETALE MAPS 10
1.6 PRE-3-FILTRATIONS OF SHEAVES 11
1.7 J-FILTRATIONS OF SHEAVES (THE HAUSDORFF CASE) 13
1.8 J-FILTERED LOCAL SYSTEMS (THE HAUSDORFF CASE) 16
1.9 J-FILTERED LOCAL SYSTEMS (THE STRATIFIED HAUSDORFF CASE) 16 1.10
COMMENTS 19
PART I DIMENSION ONE
2 STOKES-FILTERED LOCAL SYSTEMS IN DIMENSION ONE 23
2.1 INTRODUCTION 23
2.2 NON-RAMIFIED STOKES-FILTERED LOCAL SYSTEMS 23
2.3 PULL-BACK AND PUSH-FORWARD 29
2.4 STOKES FILTRATIONS ON LOCAL SYSTEMS 31
2.5 EXTENSION OF SCALARS 35
2.6 STOKES-FILTERED LOCAL SYSTEMS AND STOKES DATA 36
3 ABELIANITY AND STRICTNESS 39
3.1 INTRODUCTION 39
3.2 STRICTNESS AND ABELIANITY 40
3.3 LEVEL STRUCTURE OF A STOKES-FILTERED LOCAL SYSTEM 41
3.4 PROOF OF THEOREM 3.5 43
3.5 PROOF OF THE STABILITY BY EXTENSION 48
3.6 MORE ON THE LEVEL STRUCTURE 48
3.7 COMMENTS 49
V
HTTP://D-NB.INFO/1023292297
IMAGE 2
VI C O N T E N T S
4 STOKES-PERVERSE SHEAVES ON RIEMANN SURFACES 51
4.1 INTRODUCTION 51
4.2 THE SETTING 52
4.3 THE CATEGORY OF STOKES-C-CONSTRUCTIBLE SHEAVES ON X 53
4.4 DERIVED CATEGORIES AND DUALITY 55
4.5 THE CATEGORY OF STOKES-PERVERSE SHEAVES ON X 58
4.6 DIRECT IMAGE TO X 60
4.7 STOKES-PERVERSE SHEAVES ON X_ 60
4.8 ASSOCIATED PERVERSE SHEAF ON I 62
5 THE RIEMANN-HILBERT CORRESPONDENCE FOR HOLONOMIC ^-MODULES ON CURVES
65
5.1 INTRODUCTION 65
5.2 SOME BASIC SHEAVES 66
5.3 THE RIEMANN-HILBERT CORRESPONDENCE FOR GERMS 68
5.4 THE RIEMANN-HILBERT CORRESPONDENCE IN THE GLOBAL CASE 75 5.5
COMPATIBILITY WITH DUALITY FOR MEROMORPHIC CONNECTIONS 77
6 APPLICATIONS O F THE RIEMANN-HILBERT CORRESPONDENCE TO HOLONOMIC
DISTRIBUTIONS 79
6.1 INTRODUCTION 79
6.2 THE RIEMANN-HILBERT CORRESPONDENCE FOR MEROMORPHIC CONNECTIONS OF
HUKUHARA-TURRITTIN TYPE 80 6.3 THE HERMITIAN DUAL OF A HOLONOMIC ^ - M O
D U L E 81
6.4 ASYMPTOTIC EXPANSIONS OF HOLONOMIC DISTRIBUTIONS 82
6.5 COMMENTS 88
7 RIEMANN-HILBERT AND LAPLACE ON THE AFFINE LINE (THE REGULAR CASE) 89
7.1 INTRODUCTION 89
7.2 DIRECT IMAGE OF THE MODERATE DE RHAM COMPLEX 91
7.3 TOPOLOGICAL SPACES 95
7.4 TOPOLOGICAL LAPLACE TRANSFORM 97
7.5 PROOF OF THEOREM 7.6 AND COMPATIBILITY WITH RIEMANN-HILBERT 101
7.6 COMPATIBILITY OF LAPLACE TRANSFORMATION WITH DUALITY 103 7.7
COMPATIBILITY OF TOPOLOGICAL LAPLACE TRANSFORMATION WITH
POINCARE-VERDIER DUALITY 105
7.8 COMPARISON OF BOTH DUALITY ISOMORPHISMS 108
PART II DIMENSION TWO AND MORE
8 REAL BLOW-UP SPACES AND MODERATE DE RHAM COMPLEXES 115 8.1
INTRODUCTION 115
8.2 REAL BLOW-UP 116
IMAGE 3
C O N T E N T S V I I
8.3 THE SHEAF OF FUNCTIONS WITH MODERATE GROWTH
ON THE REAL BLOW-UP SPACE 118
8.4 THE MODERATE DE RHAM COMPLEX 121
8.5 EXAMPLES OF MODERATE DE RHAM COMPLEXES 127
9 STOKES-FILTERED LOCAL SYSTEMS ALONG A DIVISOR WITH NORMAL CROSSINGS
131
9.1 INTRODUCTION 131
9.2 THE SHEAF 3 ON THE REAL BLOW-UP (SMOOTH DIVISOR CASE) 132 9.3 THE
SHEAF J ON THE REAL BLOW-UP (NORMAL CROSSING CASE) 133 9.4 GOODNESS 134
9.5 STOKES FILTRATIONS ON LOCAL SYSTEMS 138
9.6 BEHAVIOUR BY PULL-BACK 142
9.7 PARTIALLY REGULAR STOKES-FILTERED LOCAL SYSTEMS 145
10 THE RIEMANN-HILBERT CORRESPONDENCE FOR GOOD MEROMORPHIC CONNECTIONS
(CASE OF A SMOOTH DIVISOR) 147 10.1 INTRODUCTION 147
10.2 GOOD FORMAL STRUCTURE OF A MEROMORPHIC CONNECTION 149 10.3 THE
RIEMANN-HILBERT FUNCTOR 150
10.4 PROOF OF THE FULL FAITHFULNESS IN THEOREM 10.8 152
10.5 ELEMENTARY AND GRADED EQUIVALENCES 153
10.6 PROOF OF THE ESSENTIAL SURJECTIVITY IN THEOREM 10.8 155
11 GOOD MEROMORPHIC CONNECTIONS (FORMAL THEORY) 159
11.1 INTRODUCTION 159
11.2 PRELIMINARY NOTATION 160
11.3 GOOD FORMAL DECOMPOSITION 161
11.4 GOOD LATTICES 166
11.5 PROOF OF THEOREM 11.18 168
11.6 COMMENTS 175
12 GOOD MEROMORPHIC CONNECTIONS (ANALYTIC THEORY) AND THE
RIEMANN-HILBERT CORRESPONDENCE 177
12.1 INTRODUCTION 177
12.2 NOTATION 178
12.3 THE MALGRANGE-SIBUYA THEOREM IN HIGHER DIMENSION 179 12.4 THE
HIGHER DIMENSIONAL HUKUHARA-TURRITTIN THEOREM 181 12.5 THE
RIEMANN-HILBERT CORRESPONDENCE 188
12.6 APPLICATION TO HERMITIAN DUALITY OF HOLONOMIC ^-MODULES 191 12.7
COMMENTS 192
13 PUSH-FORWARD O F STOKES-FILTERED LOCAL SYSTEMS 195
13.1 INTRODUCTION 195
13.2 PRELIMINARIES 196
13.3 ADJUNCTION 197
13.4 RECENT ADVANCES ON PUSH-FORWARD AND OPEN QUESTIONS 198
IMAGE 4
VIII C O N T E N T S
13.5 AN EXAMPLE OF PUSH-FORWARD COMPUTATION 199
13.6 THE TOPOLOGICAL COMPUTATION OF THE STOKES FILTRATION: LEAKY PIPES
201
14 IRREGULAR NEARBY CYCLES 207
14.1 INTRODUCTION 207
14.2 MODERATE NEARBY CYCLES OF HOLONOMIC ^-MODULES 208
14.3 IRREGULAR NEARBY CYCLES (AFTER DELIGNE) 213
14.4 ANOTHER PROOF OF THE FINITENESS THEOREM IN DIMENSION TWO 214
15 NEARBY CYCLES OF STOKES-FILTERED LOCAL SYSTEMS 227
15.1 INTRODUCTION 227
15.2 NEARBY CYCLES ALONG A FUNCTION (THE GOOD CASE) 228
15.3 NEARBY CYCLES ALONG A FUNCTION (DIMENSION TWO) 231
15.4 COMPARISON 236
REFERENCES 239
INDEX O F NOTATION 245
INDEX 247 |
| any_adam_object | 1 |
| author | Sabbah, Claude 1954- |
| author_GND | (DE-588)141260785 |
| author_facet | Sabbah, Claude 1954- |
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| ctrlnum | (OCoLC)816294154 (DE-599)DNB1023292297 |
| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 3642316948 9783642316944 |
| language | English |
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| spelling | Sabbah, Claude 1954- Verfasser (DE-588)141260785 aut Introduction to Stokes structures Claude Sabbah Berlin [u.a.] Springer 2013 XIV, 249 S. Ill., graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2060 Stokes-Phänomen (DE-588)4769592-4 gnd rswk-swf Stokes-Phänomen (DE-588)4769592-4 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-31695-1 Lecture notes in mathematics 2060 (DE-604)BV000676446 2060 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4056624&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025343849&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sabbah, Claude 1954- Introduction to Stokes structures Lecture notes in mathematics Stokes-Phänomen (DE-588)4769592-4 gnd |
| subject_GND | (DE-588)4769592-4 |
| title | Introduction to Stokes structures |
| title_auth | Introduction to Stokes structures |
| title_exact_search | Introduction to Stokes structures |
| title_full | Introduction to Stokes structures Claude Sabbah |
| title_fullStr | Introduction to Stokes structures Claude Sabbah |
| title_full_unstemmed | Introduction to Stokes structures Claude Sabbah |
| title_short | Introduction to Stokes structures |
| title_sort | introduction to stokes structures |
| topic | Stokes-Phänomen (DE-588)4769592-4 gnd |
| topic_facet | Stokes-Phänomen |
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