Quaternion orders, quadratic forms, and Shimura curves:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
2004
|
| Schriftenreihe: | CRM monograph series
22 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVI, 196 S. graph. Darst. |
| ISBN: | 0821833596 |
Internformat
MARC
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| 245 | 1 | 0 | |a Quaternion orders, quadratic forms, and Shimura curves |c Montserrat Alsina ; Pilar Bayer |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2004 | |
| 300 | |a XVI, 196 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a CRM monograph series |v 22 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Formes quadratiques | |
| 650 | 4 | |a Quaternions | |
| 650 | 4 | |a Shimura, Variétés de | |
| 650 | 4 | |a Forms, Quadratic | |
| 650 | 4 | |a Quaternions | |
| 650 | 4 | |a Shimura varieties | |
| 650 | 0 | 7 | |a Shimura-Mannigfaltigkeit |0 (DE-588)4181143-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quadratische Form |0 (DE-588)4128297-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Quadratische Form |0 (DE-588)4128297-8 |D s |
| 689 | 0 | 2 | |a Shimura-Mannigfaltigkeit |0 (DE-588)4181143-4 |D s |
| 689 | 0 | |C b |5 DE-604 | |
| 700 | 1 | |a Bayer i Isant, Pilar |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-012816971 | ||
Datensatz im Suchindex
| _version_ | 1804132783895871488 |
|---|---|
| adam_text | Contents
List of Tables vii
List of Figures x;
Introduction xiii
Chapter 1. Quaternion Algebras and Quaternion Orders 1
1.1. Introduction to quaternion algebras 1
1.2. Introduction to quaternion orders 7
Chapter 2. Introduction to Shimura Curves 17
2.1. The Poincare half plane 17
2.2. Linear fractional transformations 18
2.3. Groups of quaternion transformations 22
2.4. The Shimura curves X(D,N) 24
Chapter 3. Quaternion Algebras and Quadratic Forms 27
3.1. Quadratic forms over rings 27
3.2. Principal forms 33
3.3. Quadratic forms associated to /( algebras 38
3.4. Quadratic forms associated to quadratic fields and orders 40
3.5. Normic forms of quaternion algebras 43
3.6. Normic forms of quaternion orders 49
Chapter 4. Embeddings and Quadratic Forms 55
4.1. Embeddings of quadratic fields into quaternion algebras 55
4.2. Embeddings of quadratic orders into quaternion orders 57
4.3. Classification of representations by normic ternary forms 61
4.4. Binary forms associated to quaternion orders 67
4.5. Classification of binary forms associated to quaternion orders 71
Chapter 5. Hyperbolic Fundamental Domains for Shimura Curves 77
5.1. Fundamental domains of modular curves 77
5.2. Transformations, embeddings and forms 79
5.3. Local conditions at infinity 86
5.4. Principal symmetries of F(D, N) 89
5.5. Construction of fundamental domains (D 1) 91
Chapter 6. Complex Multiplication Points in Shimura Curves 103
6.1. Classification of complex multiplication points 103
6.2. Special complex multiplication points 108
6.3. Computation of complex multiplication points 109
v
vi CONTENTS
6.4. Examples in the nonramified case 112
6.5. Examples in the small ramified case 120
Chapter 7. The Poincare Package 123
7.1. Main characteristics 123
7.2. Description of the instructions 124
7.3. List of instructions 130
Appendix A. Tables 145
A.I. Quaternion algebras 145
A.2. Shimura curves 153
A.3. Quaternion algebras and quadratic forms 160
A.4. Embeddings and quadratic forms 165
A.5. Complex multiplication points in Shimura curves 183
Appendix B. Further Contributions to the Study of Shimura Curves 187
Appendix C. Applications of Shimura Curves 189
Bibliography 191
Index 195
|
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| id | DE-604.BV019352957 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:58:19Z |
| institution | BVB |
| isbn | 0821833596 |
| language | English |
| lccn | 2004040995 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012816971 |
| oclc_num | 54035139 |
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| owner | DE-355 DE-BY-UBR DE-703 DE-11 |
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| physical | XVI, 196 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | CRM monograph series |
| series2 | CRM monograph series |
| spelling | Alsina, Montserrat Verfasser aut Quaternion orders, quadratic forms, and Shimura curves Montserrat Alsina ; Pilar Bayer Providence, R.I. American Mathematical Society 2004 XVI, 196 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier CRM monograph series 22 Includes bibliographical references and index Formes quadratiques Quaternions Shimura, Variétés de Forms, Quadratic Shimura varieties Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd rswk-swf Quadratische Form (DE-588)4128297-8 gnd rswk-swf Quaternionenalgebra (DE-588)4618620-7 gnd rswk-swf Quaternionenalgebra (DE-588)4618620-7 s Quadratische Form (DE-588)4128297-8 s Shimura-Mannigfaltigkeit (DE-588)4181143-4 s b DE-604 Bayer i Isant, Pilar Verfasser aut CRM monograph series 22 (DE-604)BV007928388 22 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012816971&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alsina, Montserrat Bayer i Isant, Pilar Quaternion orders, quadratic forms, and Shimura curves CRM monograph series Formes quadratiques Quaternions Shimura, Variétés de Forms, Quadratic Shimura varieties Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Quadratische Form (DE-588)4128297-8 gnd Quaternionenalgebra (DE-588)4618620-7 gnd |
| subject_GND | (DE-588)4181143-4 (DE-588)4128297-8 (DE-588)4618620-7 |
| title | Quaternion orders, quadratic forms, and Shimura curves |
| title_auth | Quaternion orders, quadratic forms, and Shimura curves |
| title_exact_search | Quaternion orders, quadratic forms, and Shimura curves |
| title_full | Quaternion orders, quadratic forms, and Shimura curves Montserrat Alsina ; Pilar Bayer |
| title_fullStr | Quaternion orders, quadratic forms, and Shimura curves Montserrat Alsina ; Pilar Bayer |
| title_full_unstemmed | Quaternion orders, quadratic forms, and Shimura curves Montserrat Alsina ; Pilar Bayer |
| title_short | Quaternion orders, quadratic forms, and Shimura curves |
| title_sort | quaternion orders quadratic forms and shimura curves |
| topic | Formes quadratiques Quaternions Shimura, Variétés de Forms, Quadratic Shimura varieties Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Quadratische Form (DE-588)4128297-8 gnd Quaternionenalgebra (DE-588)4618620-7 gnd |
| topic_facet | Formes quadratiques Quaternions Shimura, Variétés de Forms, Quadratic Shimura varieties Shimura-Mannigfaltigkeit Quadratische Form Quaternionenalgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012816971&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007928388 |
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