Rational points on modular elliptic curves:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2004
|
| Series: | Regional conference series in mathematics
101 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references Includes bibliographical references |
| Physical Description: | XII, 129 S. |
| ISBN: | 0821828681 |
Staff View
MARC
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| 100 | 1 | |a Darmon, Henri |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Rational points on modular elliptic curves |c Henri Darmon |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2004 | |
| 300 | |a XII, 129 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Regional conference series in mathematics |v 101 | |
| 500 | |a Includes bibliographical references | ||
| 500 | |a Includes bibliographical references | ||
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| 650 | 4 | |a Modular curves | |
| 650 | 4 | |a Rational points (Geometry) | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
Chapter
1.
Elliptic curves
1
1.1.
Elliptic curves
1
1.2.
The Mordell-Weil theorem
3
1.3.
The Birch and Swinnerton-Dyer conjecture
6
1.4.
L-functions
7
1.5.
Some known results
8
Further results and references
9
Exercises
10
Chapter
2.
Modular forms
13
2.1.
Modular forms
13
2.2. Hecke
operators
14
2.3.
Atkin-Lehner theory
16
2.4.
L-series
17
2.5.
Eichler-Shimura theory
18
2.6.
Wiles theorem
20
2.7.
Modular symbols
21
Further results and references
25
Exercises
26
Chapter
3.
Heegner points on X0(N)
29
3.1.
Complex multiplication
29
3.2.
Heegner points
33
3.3.
Numerical examples
34
3.4.
Properties of Heegner points
35
3.5.
Heegner systems
36
3.6.
Relation with the Birch and Swinnertoii-Dyer conjecture
37
3.7.
The Gross-Zagier formula 39
3.8.
Kolyvagin s theorem
^0
3.9.
Proof of the Gross-Zagier-Kolyvagin theorem
40
Further results
41
Exercises
Chapter
4.
Heegner points on Shimura curves
45
4.1.
Quaternion algebras
4.2.
Modular forms on quaternion algebras
47
4.3.
Shimura curves
4.4.
The Eichler-Shimura construction, revisited
50
viii CONTENTS
4.5.
The Jacquet-Langlands correspondence
50
4.6.
The Shimirra-Taniyama-Weil conjecture, revisited
51
4.7.
Complex multiplication for
Н/Гдг+^у-
51
4.8.
Heegner systems
52
4.9.
The Gross-Zagier formula
53
References
54
Exercises
54
Chapter
5.
Rigid analytic modular forms
57
5.1.
p-adic
uniformisation
57
5.2.
Rigid analytic modular forms
60
5.8.
p-adic line integrals
63
Further results
65
Exercises
65
Chapter
6.
Rigid analytic modular parametrisations
67
6.1.
Rigid analytic modular forms on quaternion algebras
67
6.2.
The
Čerednik-Drinfeld
theorem
68
6.3.
The p-adic Shimura-Taniyama-Weil conjecture
68
6.4.
Complex multiplication, revisited
69
6.5.
An example
70
6.6.
p-adic L-functions,
d après
Schneider-Iovita-Spiess
73
6.7.
A Gross-Zagier formula
74
Further results
75
Exercises
75
Chapter
7.
Totally real fields
79
7.1.
Elliptic curves over number fields
79
7.2.
Hubert modular forms
80
7.3.
The Shimura-Taniyama-Weil conjecture
82
7.4.
The Eichler-Shimura construction for totally real fields
83
7.5.
The Heegner construction
84
7.6.
A preview of Chapter
8 85
Further results
86
Chapter
8.
ATR points
87
8.1.
Period integrals
87
8.2.
Generalities on group cohomoiogy
88
8.3.
The cohomoiogy of Hilbert modular groups
89
8.4.
ATR points
93
References
95
Exercises
95
Chapter
9.
Integration on TLp
χ Η
97
9.1.
Discrete arithmetic subgroups of SL2(Qj,)
x
SL2(R)
98
9.2.
Forms
опПРхН
. 99
9.3.
Periods
101
9.4.
Some p-adic cocycles
104
9.5.
Stark-Heegner points
105
9.6.
Computing Stark-Heegner points
106
CONTENTS ix
Further results
109
Exercises
1.09
Chapter
10.
Kolyvagin s theorem
113
10.1.
Bounding
Selmer
groups
114
10.2.
Kolyvagin cohomology classes
117
10.3.
Proof of Kolyvagin s theorem
121
References
122
Exercises
122
Bibliography
125
|
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| ctrlnum | (OCoLC)53461969 (DE-599)BVBBV017683194 |
| dewey-full | 510 516.3/52 516.352 |
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| dewey-ones | 510 - Mathematics 516 - Geometry |
| dewey-raw | 510 516.3/52 516.352 |
| dewey-search | 510 516.3/52 516.352 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017683194 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:20:43Z |
| institution | BVB |
| isbn | 0821828681 |
| language | English |
| lccn | 2003063735 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010632171 |
| oclc_num | 53461969 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-188 |
| physical | XII, 129 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Regional conference series in mathematics |
| series2 | Regional conference series in mathematics |
| spelling | Darmon, Henri Verfasser aut Rational points on modular elliptic curves Henri Darmon Providence, R.I. American Mathematical Society 2004 XII, 129 S. txt rdacontent n rdamedia nc rdacarrier Regional conference series in mathematics 101 Includes bibliographical references Curves, Elliptic Modular curves Rational points (Geometry) Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Rationaler Punkt (DE-588)4177004-3 gnd rswk-swf Rationaler Punkt (DE-588)4177004-3 s Elliptische Kurve (DE-588)4014487-2 s DE-604 Regional conference series in mathematics 101 (DE-604)BV000004346 101 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010632171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Darmon, Henri Rational points on modular elliptic curves Regional conference series in mathematics Curves, Elliptic Modular curves Rational points (Geometry) Elliptische Kurve (DE-588)4014487-2 gnd Rationaler Punkt (DE-588)4177004-3 gnd |
| subject_GND | (DE-588)4014487-2 (DE-588)4177004-3 |
| title | Rational points on modular elliptic curves |
| title_auth | Rational points on modular elliptic curves |
| title_exact_search | Rational points on modular elliptic curves |
| title_full | Rational points on modular elliptic curves Henri Darmon |
| title_fullStr | Rational points on modular elliptic curves Henri Darmon |
| title_full_unstemmed | Rational points on modular elliptic curves Henri Darmon |
| title_short | Rational points on modular elliptic curves |
| title_sort | rational points on modular elliptic curves |
| topic | Curves, Elliptic Modular curves Rational points (Geometry) Elliptische Kurve (DE-588)4014487-2 gnd Rationaler Punkt (DE-588)4177004-3 gnd |
| topic_facet | Curves, Elliptic Modular curves Rational points (Geometry) Elliptische Kurve Rationaler Punkt |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010632171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
| work_keys_str_mv | AT darmonhenri rationalpointsonmodularellipticcurves |