Abelian varieties with complex multiplication and modular functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton Univ. Press
1998
|
| Series: | Princeton mathematical series
46 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 217 S. |
| ISBN: | 0691016569 |
Staff View
MARC
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| 245 | 1 | 0 | |a Abelian varieties with complex multiplication and modular functions |c Goro Shimura |
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Record in the Search Index
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| adam_text | Contents
Preface vii
Preface to Complex Multiplication ofAbelian
Varieties and Its Applications to Number Theory
(1961) ix
Notation and Terminology xiii
Chapter I. Preliminaries on Abelian Varieties 3
1. Homomorphisms and divisors 3
2. Differential forms 7
3. Analytic theory of abelian varieties 19
4. Fields of moduli and Kummer varieties 25
Chapter II. Abelian Varieties with Complex Multiplication 35
5. Structure of endomorphism algebras 35
6. Construction of abelian varieties with
complex multiplication 40
7. Transformations and multiplications 47
8. The reflex of a CM type 58
Chapter III. Reduction of Constant Fields 68
9. Reduction of varieties and cycles 68
10. Reduction of rational mappings and differential forms 74
11. Reduction of abelian varieties 83
12. The theory for almost all p 87
13. The prime ideal decomposition of an /V(p) th
power homomorphism 96
Chapter IV. Construction of Class Fields 101
14. Polarized abelian varieties of type (K: ip,)) 101
15. The unramified class field obtained from the field
of moduli 109
16. The class fields generated by ideal section points 114
17. The field of moduli in a generalized setting 118
18. The main theorem of complex multiplication in the
adelic language 121
v
VI CONTENTS
Chapter V. The Zeta Function of an Abelian Variety with
Complex Multiplication 132
19. The zeta function relative to a field over which some
endomorphisms are defined 132
20. The zeta function over smaller fields 137
21. Models over the field of moduli and models with
given Hecke characters 145
22. The case of elliptic curves 149
Chapter VI. Families of Abelian Varieties and
Modular Functions 151
23. Symplectic and unitary groups 151
24. Families of polarized abelian varieties 156
25. Modular forms and functions 165
26. Canonical models 169
Chapter VII. Theta Functions and Periods on Abelian Varieties 173
27. Theta functions 173
28. Proof of Theorem 27.7 and Proposition 27.9 181
29. Theta functions with complex multiplication 188
30. The periods of differential forms on abelian varieties 190
31. Periods in the Hilbert modular case 193
32. Periods on abelian varieties with complex
multiplication and their algebraic relations 196
33. Proof of Theorem 32.4 201
Bibliography 209
Supplementary References 213
Index 215
|
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| id | DE-604.BV011754493 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:15:14Z |
| institution | BVB |
| isbn | 0691016569 |
| language | English |
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| physical | XIV, 217 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Princeton mathematical series |
| series2 | Princeton mathematical series |
| spelling | Shimura, Goro 1930-2019 Verfasser (DE-588)12425067X aut Abelian varieties with complex multiplication and modular functions Goro Shimura Princeton, NJ Princeton Univ. Press 1998 XIV, 217 S. txt rdacontent n rdamedia nc rdacarrier Princeton mathematical series 46 Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd rswk-swf Komplexe Multiplikation (DE-588)4164903-5 gnd rswk-swf Modulfunktion (DE-588)4039855-9 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 s Komplexe Multiplikation (DE-588)4164903-5 s Modulfunktion (DE-588)4039855-9 s DE-604 Princeton mathematical series 46 (DE-604)BV000019035 46 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007932112&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shimura, Goro 1930-2019 Abelian varieties with complex multiplication and modular functions Princeton mathematical series Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Komplexe Multiplikation (DE-588)4164903-5 gnd Modulfunktion (DE-588)4039855-9 gnd |
| subject_GND | (DE-588)4140992-9 (DE-588)4164903-5 (DE-588)4039855-9 |
| title | Abelian varieties with complex multiplication and modular functions |
| title_auth | Abelian varieties with complex multiplication and modular functions |
| title_exact_search | Abelian varieties with complex multiplication and modular functions |
| title_full | Abelian varieties with complex multiplication and modular functions Goro Shimura |
| title_fullStr | Abelian varieties with complex multiplication and modular functions Goro Shimura |
| title_full_unstemmed | Abelian varieties with complex multiplication and modular functions Goro Shimura |
| title_short | Abelian varieties with complex multiplication and modular functions |
| title_sort | abelian varieties with complex multiplication and modular functions |
| topic | Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Komplexe Multiplikation (DE-588)4164903-5 gnd Modulfunktion (DE-588)4039855-9 gnd |
| topic_facet | Abelsche Mannigfaltigkeit Komplexe Multiplikation Modulfunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007932112&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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