Elliptic curves and big Galois representations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | London mathematical society lecture note series
356 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 281 S. |
| ISBN: | 9780521728669 |
Internformat
MARC
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| 100 | 1 | |a Delbourgo, Daniel |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elliptic curves and big Galois representations |c Daniel Delbourgo |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a IX, 281 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London mathematical society lecture note series |v 356 | |
| 650 | 4 | |a Curves, Elliptic | |
| 650 | 4 | |a Galois theory | |
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Datensatz im Suchindex
| _version_ | 1804137937971970048 |
|---|---|
| adam_text | Contents
Introduction
1
List of
Notations
6
Chapter I
Background
7
1.1
Elliptic curves
8
1.2
Hasse-Weil ¿-functions IS
1.3
Structure of the Mordell-Weil group
18
1.4
The conjectures of Birch and Swinnerton-Dyer
22
1.5
Modular forms and
Hecke
algebras
26
Chapter II
p-Adic i-functions and
Zeta
Elements
31
2.1
The p-adic Birch and Swinnerton-Dyer conjecture
31
2.2
Perrin-Riou s local Iwasawa theory
34
2.3
Integrality and
(φ,
r)-modules
39
2.4
Norm relations in if-theory
43
2.5
Kato s p-adic zeta-elements
46
Chapter III
Cyclotomic Deformations of Modular Symbols
50
3.1
Q-continuity
50
3.2
Cohomological subspaces of
Euler
systems
56
3.3
The one-variable interpolation
60
3.4
Local freeness of the image
64
Chapter IV
A User s Guide to Hida Theory
70
4.1
The universal ordinary Galois representation
70
4.2
А
-adic
modular forms
72
4.3
Multiplicity one for I-adic modular symbols
76
4.4
Two-variable p-adic L-functions
80
viii Contents
Chapter V
Crystalline Weight Deformations
86
5.1
Cohomologies over deformation rings
87
5.2
p-Ordinary deformations of Bens and D^s
92
5.3
Constructing big dual exponentials
96
5.4
Local dualities
101
Chapter VI
Super Zeta-Elements
108
6.1
The
Тг
-adic
version of Kato s theorem
109
6.2
A two-variable interpolation
118
6.3
Applications to Iwasawa theory
128
6.4
The Coleman exact sequence
132
6.5
Computing the
Tčirj-torsion
137
Chapter
VII
Vertical and Half-Twisted Arithmetic
141
7.1
Big
Selmer
groups
142
7.2
The fundamental commutative diagrams
147
7.3
Control theory for
Selmer coranks
159
Chapter
VIII
Diamond-Euler Characteristics: the Local Case
165
8.1
Analytic rank zero
166
8.2
The Tamagawa factors away
from p
169
8.3
The Tamagawa factors above
ρ
(the vertical case)
173
8.4
The Tamagawa factors above
ρ
(the half-twisted case)
180
8.5
Evaluating the covolumes
183
Chapter IX
Diamond-Euler Characteristics: the Global Case
191
9.1
The Poitou-Tate exact sequences
192
9.2
Triviality of the compact
Selmer
group
197
9.3
The p-adic weight pairings
201
9.4
Commutativity of the bottom squares
208
9.5
The leading term of IIIF (Too.je)
214
9.6
Variation under the isogeny
ϋ
:
E
-*
C 1
219
Contents ix
Chapter X
Two-Variable Iwasawa Theory of Elliptic Curves
222
10.1
The half-twisted
Euler
characteristic formula
223
10.2
The p-adic height over a double deformation
228
10.3
Behaviour of the characteristic ideals
230
10.4
The proof of Theorems
10.8
and
10.11 234
10.5
The main conjectures over weight-space
243
10.6
Numerical examples, open problems
246
Appendices
A: The
Primitivity
of
Zeta
Elements
252
B: Specialising the Universal Path Vector
257
C: The Weight-Variable Control Theorem (by Paul A. Smith)
260
C.I Notation and assumptions
260
C.2 Properties of affinoids
262
C.3 The cohomology of a lattice
L
264
C.4 Local conditions
265
C.5 Dualities via the Ext-pairings
269
C.6 Controlling the
Selmer
groups
273
Bibliography
275
Index
280
|
| adam_txt |
Contents
Introduction
1
List of
Notations
6
Chapter I
Background
7
1.1
Elliptic curves
8
1.2
Hasse-Weil ¿-functions IS
1.3
Structure of the Mordell-Weil group
18
1.4
The conjectures of Birch and Swinnerton-Dyer
22
1.5
Modular forms and
Hecke
algebras
26
Chapter II
p-Adic i-functions and
Zeta
Elements
31
2.1
The p-adic Birch and Swinnerton-Dyer conjecture
31
2.2
Perrin-Riou's local Iwasawa theory
34
2.3
Integrality and
(φ,
r)-modules
39
2.4
Norm relations in if-theory
43
2.5
Kato's p-adic zeta-elements
46
Chapter III
Cyclotomic Deformations of Modular Symbols
50
3.1
Q-continuity
50
3.2
Cohomological subspaces of
Euler
systems
56
3.3
The one-variable interpolation
60
3.4
Local freeness of the image
64
Chapter IV
A User's Guide to Hida Theory
70
4.1
The universal ordinary Galois representation
70
4.2
А
-adic
modular forms
72
4.3
Multiplicity one for I-adic modular symbols
76
4.4
Two-variable p-adic L-functions
80
viii Contents
Chapter V
Crystalline Weight Deformations
86
5.1
Cohomologies over deformation rings
87
5.2
p-Ordinary deformations of Bens and D^s
92
5.3
Constructing big dual exponentials
96
5.4
Local dualities
101
Chapter VI
Super Zeta-Elements
108
6.1
The
Тг
-adic
version of Kato's theorem
109
6.2
A two-variable interpolation
118
6.3
Applications to Iwasawa theory
128
6.4
The Coleman exact sequence
132
6.5
Computing the
Tčirj-torsion
137
Chapter
VII
Vertical and Half-Twisted Arithmetic
141
7.1
Big
Selmer
groups
142
7.2
The fundamental commutative diagrams
147
7.3
Control theory for
Selmer coranks
159
Chapter
VIII
Diamond-Euler Characteristics: the Local Case
165
8.1
Analytic rank zero
166
8.2
The Tamagawa factors away
from p
169
8.3
The Tamagawa factors above
ρ
(the vertical case)
173
8.4
The Tamagawa factors above
ρ
(the half-twisted case)
180
8.5
Evaluating the covolumes
183
Chapter IX
Diamond-Euler Characteristics: the Global Case
191
9.1
The Poitou-Tate exact sequences
192
9.2
Triviality of the compact
Selmer
group
197
9.3
The p-adic weight pairings
201
9.4
Commutativity of the bottom squares
208
9.5
The leading term of IIIF (Too.je)
214
9.6
Variation under the isogeny
ϋ
:
E
-*
C"1'"
219
Contents ix
Chapter X
Two-Variable Iwasawa Theory of Elliptic Curves
222
10.1
The half-twisted
Euler
characteristic formula
223
10.2
The p-adic height over a double deformation
228
10.3
Behaviour of the characteristic ideals
230
10.4
The proof of Theorems
10.8
and
10.11 234
10.5
The main conjectures over weight-space
243
10.6
Numerical examples, open problems
246
Appendices
A: The
Primitivity
of
Zeta
Elements
252
B: Specialising the Universal Path Vector
257
C: The Weight-Variable Control Theorem (by Paul A. Smith)
260
C.I Notation and assumptions
260
C.2 Properties of affinoids
262
C.3 The cohomology of a lattice
L
264
C.4 Local conditions
265
C.5 Dualities via the Ext-pairings
269
C.6 Controlling the
Selmer
groups
273
Bibliography
275
Index
280 |
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| id | DE-604.BV035015173 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:45:10Z |
| indexdate | 2024-07-09T21:20:14Z |
| institution | BVB |
| isbn | 9780521728669 |
| language | English |
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| series | London mathematical society lecture note series |
| series2 | London mathematical society lecture note series |
| spelling | Delbourgo, Daniel Verfasser aut Elliptic curves and big Galois representations Daniel Delbourgo 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 IX, 281 S. txt rdacontent n rdamedia nc rdacarrier London mathematical society lecture note series 356 Curves, Elliptic Galois theory Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Galois-Darstellung (DE-588)4221407-5 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Galois-Darstellung (DE-588)4221407-5 s DE-604 London mathematical society lecture note series 356 (DE-604)BV000000130 356 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016684353&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Delbourgo, Daniel Elliptic curves and big Galois representations London mathematical society lecture note series Curves, Elliptic Galois theory Elliptische Kurve (DE-588)4014487-2 gnd Galois-Darstellung (DE-588)4221407-5 gnd |
| subject_GND | (DE-588)4014487-2 (DE-588)4221407-5 |
| title | Elliptic curves and big Galois representations |
| title_auth | Elliptic curves and big Galois representations |
| title_exact_search | Elliptic curves and big Galois representations |
| title_exact_search_txtP | Elliptic curves and big Galois representations |
| title_full | Elliptic curves and big Galois representations Daniel Delbourgo |
| title_fullStr | Elliptic curves and big Galois representations Daniel Delbourgo |
| title_full_unstemmed | Elliptic curves and big Galois representations Daniel Delbourgo |
| title_short | Elliptic curves and big Galois representations |
| title_sort | elliptic curves and big galois representations |
| topic | Curves, Elliptic Galois theory Elliptische Kurve (DE-588)4014487-2 gnd Galois-Darstellung (DE-588)4221407-5 gnd |
| topic_facet | Curves, Elliptic Galois theory Elliptische Kurve Galois-Darstellung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016684353&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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