Rigid local systems:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
1996
|
| Schriftenreihe: | Annals of Mathematics Studies
139 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007189394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | VII, 223 Seiten |
| ISBN: | 0691011192 0691011184 |
Internformat
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| 100 | 1 | |a Katz, Nicholas M. |d 1943- |e Verfasser |0 (DE-588)141265558 |4 aut | |
| 245 | 1 | 0 | |a Rigid local systems |c by Nicholas M. Katz |
| 264 | 1 | |a Princeton, NJ |b Princeton University Press |c 1996 | |
| 300 | |a VII, 223 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Annals of Mathematics Studies |v 139 | |
| 650 | 7 | |a Differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Equations différentielles - Solutions numériques |2 ram | |
| 650 | 4 | |a Faisceaux, Théorie des | |
| 650 | 7 | |a Faisceaux, théorie des |2 ram | |
| 650 | 4 | |a Fonctions hypergéométriques | |
| 650 | 7 | |a Fonctions hypergéométriques |2 ram | |
| 650 | 7 | |a Schoven (Topologie) |2 gtt | |
| 650 | 4 | |a Équations différentielles - Solutions numériques | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Hypergeometric functions | |
| 650 | 4 | |a Sheaf theory | |
| 650 | 0 | 7 | |a Garbentheorie |0 (DE-588)4155956-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 A 965-139 |
|---|---|
| DE-BY-TUM_katkey | 742367 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020452777 |
| _version_ | 1821931128763711488 |
| adam_text | Contents
Introduction 3
Chapter 1 First results on rigid local systems
1.0 Generalities concerning rigid local systems over C 13
1.1 The case of genus zero 14
1.2 The case of higher genus 18
1.3 The case of genus one 23
1.4 The case of genus one: detailed analysis 24
Chapter 2 The theory of middle convolution
2.0 Transition from irreducible local systems on open sets of
IP to irreducible middle extension sheaves on A . 35
2.1 Transition from irreducible middle extension sheaves on
A^ to irreducible perverse sheaves on A1 36
2.2 Review of Dbc(X, Q^) 38
2.3 Review of perverse sheaves 39
2.4 Review of Fourier Transform 45
2.5 Review of convolution 45
2.6 Convolution operators on the category of perverse sheaves:
middle convolution 47
2.7 Interlude: middle direct images (relative dimension one) 56
2.8 Middle additive convolution via middle direct image 57
2.9 Middle additive convolution with Kummer sheaves 59
2.10 Interpretation of middle additive convolution via Fourier
Transform 65
2.11 Invertible objects on A* in characteristic zero 72
2.12 Musings on «mj(j invertible objects in V in the Gm case 75
2.13 Interlude: surprising relations between m^ on A^ and
on Gm 81
2.14 Interpretive remark: Fourier Bessel Transform S3
2.15 Questions about the situation in several variables 84
2.16 Questions about the situation on elliptic curves 84
2.17 Appendix 1: the basic lemma on end exact functors 87
2.18 Appendix 2: twisting representations by characters 88
vi Contents
Chapter 3 Fourier Transform and rigidity
3.0 Fourier Transform and index of rigidity 91
3.1 Lemmas on representations of inertia groups 94
3.2 Interlude: the operation ^mid 99
3.3 Applications to middle additive convolution 100
3.4 Some open questions about local Fourier Transform 106
Chapter 4 Middle convolution: dependence on parameters
4.0 Good schemes 111
4.1 The basic setting 111
4.2 Basic results in the basic setting 112
4.3 Middle convolution in the basic setting 116
Chapter 5 Structure of rigid local systems
5.0 Cohomological rigidity 121
5.1 The category T^, and the functors MCv and MT£ 121
5.2 The main theorem on the structure of rigid local systems 125
5.3 Applications and Interpretations of the main theorem 131
5.4 Some open questions 131
5.5 Existence of universal families of rigids with given local
monodromy 132
5.6 Remark on braid groups 143
5.7 Universal families without quasiunipotence 143
5.8 The complex analytic situation 144
5.9 Return to the original question 146
Chapter 6 Existence algorithms for rigids
6.0 Numerical invariants 153
6.1 Numerical incarnation: the group NumData 156
6.2 A compatibility theorem 160
6.3 Realizable and plausible elements 161
6.4 Existence algorithm for rigids 164
6.5 An example 165
6.6 Open questions 166
6.7 Action of automorphisms 166
6.8 A remark and a question 167
Contents vii
Chapter 7 Diophantine aspects of rigidity
7.0 Diophantine criterion for irreducibility 169
7.1 Diophantine criterion for rigidity 170
7.2 Appendix: a counterexample 174
Chapter 8 Motivic description of rigids
8.0 The basic setting 183
8.1 Interlude: Kummer sheaves 184
8.2 Naive convolution on (A1 {T^, ... , Tn))sN .¦ 185
8.3 Middle convolution on (A1 {T^ ... , Tn))SN ^ 188
8.4 Geometric description of all tame rigids with
quasi unipotent local monodromy 194
8.5 A remark and a question 196
Chapter 9 Grothendieck s p curvature conjecture for rigids
9.0 Introduction 197
9.1 Review of Grothendieck s p curvature conjecture 197
9.2 Interlude: Picard Fuchs equations and some variants 199
9.3 The main result of [Ka ASDE] and a generalization 202
9.4 Application to rigid local systems 211
9.5 Comments and questions 216
References 219
|
| any_adam_object | 1 |
| author | Katz, Nicholas M. 1943- |
| author_GND | (DE-588)141265558 |
| author_facet | Katz, Nicholas M. 1943- |
| author_role | aut |
| author_sort | Katz, Nicholas M. 1943- |
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| building | Verbundindex |
| bvnumber | BV010766523 |
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| callnumber-raw | QA372 |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 141f |
| ctrlnum | (OCoLC)33281981 (DE-599)BVBBV010766523 |
| dewey-full | 515/.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.35 |
| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010766523 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:00:17Z |
| institution | BVB |
| isbn | 0691011192 0691011184 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007189394 |
| oclc_num | 33281981 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-20 DE-12 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-703 DE-634 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-20 DE-12 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-703 DE-634 DE-11 DE-188 |
| physical | VII, 223 Seiten |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spellingShingle | Katz, Nicholas M. 1943- Rigid local systems Annals of Mathematics Studies Differentiaalvergelijkingen gtt Equations différentielles - Solutions numériques ram Faisceaux, Théorie des Faisceaux, théorie des ram Fonctions hypergéométriques Fonctions hypergéométriques ram Schoven (Topologie) gtt Équations différentielles - Solutions numériques Differential equations Numerical solutions Hypergeometric functions Sheaf theory Garbentheorie (DE-588)4155956-3 gnd Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Hypergeometrische Reihe (DE-588)4161061-1 gnd |
| subject_GND | (DE-588)4155956-3 (DE-588)4012249-9 (DE-588)4128130-5 (DE-588)4161061-1 |
| title | Rigid local systems |
| title_auth | Rigid local systems |
| title_exact_search | Rigid local systems |
| title_full | Rigid local systems by Nicholas M. Katz |
| title_fullStr | Rigid local systems by Nicholas M. Katz |
| title_full_unstemmed | Rigid local systems by Nicholas M. Katz |
| title_short | Rigid local systems |
| title_sort | rigid local systems |
| topic | Differentiaalvergelijkingen gtt Equations différentielles - Solutions numériques ram Faisceaux, Théorie des Faisceaux, théorie des ram Fonctions hypergéométriques Fonctions hypergéométriques ram Schoven (Topologie) gtt Équations différentielles - Solutions numériques Differential equations Numerical solutions Hypergeometric functions Sheaf theory Garbentheorie (DE-588)4155956-3 gnd Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Hypergeometrische Reihe (DE-588)4161061-1 gnd |
| topic_facet | Differentiaalvergelijkingen Equations différentielles - Solutions numériques Faisceaux, Théorie des Faisceaux, théorie des Fonctions hypergéométriques Schoven (Topologie) Équations différentielles - Solutions numériques Differential equations Numerical solutions Hypergeometric functions Sheaf theory Garbentheorie Differentialgleichung Numerisches Verfahren Hypergeometrische Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007189394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000991 |
| work_keys_str_mv | AT katznicholasm rigidlocalsystems |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 001z 2001 A 965-139 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |