Arithmetic noncommutative geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2005]
|
| Series: | University lecture series
Volume 36 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 136 Seiten Diagramme |
| ISBN: | 0821838334 9780821838334 |
Staff View
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| 650 | 4 | |a Géométrie différentielle non commutative | |
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Record in the Search Index
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| adam_text | Contents
Foreword ix
Chapter 1. Ouverture 1
1. The NCG dictionary 3
2. Noncommutative spaces 4
3. Spectral triples 6
4. Why noncommutative geometry? 12
Chapter 2. Noncommutative modular curves 15
1. Modular curves 15
2. The noncommutative boundary of modular curves 22
3. Limiting modular symbols 27
4. Hecke eigenforms 38
5. Selberg zeta function 41
6. The modular complex and X theory of C* algebras 42
7. Intermezzo: chaotic cosmology 44
Chapter 3. Quantum statistical mechanics and Galois theory 51
1. Quantum statistical mechanics 53
2. The Bost Connes system 56
3. Noncommutative geometry and Hilbert s 12th problem 61
4. The GL2 system 64
5. Quadratic fields 70
Chapter 4. Noncommutative geometry at arithmetic infinity 81
1. Schottky uniformization 81
2. Dynamics and noncommutative geometry 88
3. Arithmetic infinity: archimedean primes 93
4. Arakelov geometry and hyperbolic geometry 97
5. Intermezzo: quantum gravity and black holes 100
6. Dual graph and noncommutative geometry 105
7. Arithmetic varieties and L factors 109
8. Archimedean cohomology 115
Chapter 5. Vistas 125
Bibliography 131
vii
|
| adam_txt |
Contents
Foreword ix
Chapter 1. Ouverture 1
1. The NCG dictionary 3
2. Noncommutative spaces 4
3. Spectral triples 6
4. Why noncommutative geometry? 12
Chapter 2. Noncommutative modular curves 15
1. Modular curves 15
2. The noncommutative boundary of modular curves 22
3. Limiting modular symbols 27
4. Hecke eigenforms 38
5. Selberg zeta function 41
6. The modular complex and X theory of C* algebras 42
7. Intermezzo: chaotic cosmology 44
Chapter 3. Quantum statistical mechanics and Galois theory 51
1. Quantum statistical mechanics 53
2. The Bost Connes system 56
3. Noncommutative geometry and Hilbert's 12th problem 61
4. The GL2 system 64
5. Quadratic fields 70
Chapter 4. Noncommutative geometry at arithmetic infinity 81
1. Schottky uniformization 81
2. Dynamics and noncommutative geometry 88
3. Arithmetic infinity: archimedean primes 93
4. Arakelov geometry and hyperbolic geometry 97
5. Intermezzo: quantum gravity and black holes 100
6. Dual graph and noncommutative geometry 105
7. Arithmetic varieties and L factors 109
8. Archimedean cohomology 115
Chapter 5. Vistas 125
Bibliography 131
vii |
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| index_date | 2024-07-02T13:18:12Z |
| indexdate | 2024-07-09T20:26:29Z |
| institution | BVB |
| isbn | 0821838334 9780821838334 |
| language | English |
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| spelling | Marcolli, Matilde 1969- Verfasser (DE-588)141750545 aut Arithmetic noncommutative geometry Matilde Marcolli. With a foreword by Yuri Manin Providence, Rhode Island American Mathematical Society [2005] © 2005 xi, 136 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 36 Géométrie différentielle non commutative Noncommutative differential geometry Nichtkommutative Differentialgeometrie (DE-588)4311174-9 gnd rswk-swf Nichtkommutative Differentialgeometrie (DE-588)4311174-9 s b DE-604 Manin, Jurij I. 1937-2023 (DE-588)121177580 wpr Erscheint auch als Online-Ausgabe 978-1-4704-2181-6 University lecture series Volume 36 (DE-604)BV004153846 36 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014167301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marcolli, Matilde 1969- Arithmetic noncommutative geometry University lecture series Géométrie différentielle non commutative Noncommutative differential geometry Nichtkommutative Differentialgeometrie (DE-588)4311174-9 gnd |
| subject_GND | (DE-588)4311174-9 |
| title | Arithmetic noncommutative geometry |
| title_auth | Arithmetic noncommutative geometry |
| title_exact_search | Arithmetic noncommutative geometry |
| title_exact_search_txtP | Arithmetic noncommutative geometry |
| title_full | Arithmetic noncommutative geometry Matilde Marcolli. With a foreword by Yuri Manin |
| title_fullStr | Arithmetic noncommutative geometry Matilde Marcolli. With a foreword by Yuri Manin |
| title_full_unstemmed | Arithmetic noncommutative geometry Matilde Marcolli. With a foreword by Yuri Manin |
| title_short | Arithmetic noncommutative geometry |
| title_sort | arithmetic noncommutative geometry |
| topic | Géométrie différentielle non commutative Noncommutative differential geometry Nichtkommutative Differentialgeometrie (DE-588)4311174-9 gnd |
| topic_facet | Géométrie différentielle non commutative Noncommutative differential geometry Nichtkommutative Differentialgeometrie |
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