Elliptic curves and big Galois representations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Edition: | 1. publ. |
| Series: | London mathematical society lecture note series
356 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 281 S. |
| ISBN: | 9780521728669 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV035015173 | ||
| 003 | DE-604 | ||
| 005 | 20111129 | ||
| 007 | t | ||
| 008 | 080821s2008 |||| 00||| eng d | ||
| 020 | |a 9780521728669 |9 978-0-521-72866-9 | ||
| 035 | |a (OCoLC)227275650 | ||
| 035 | |a (DE-599)HBZHT015605107 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-355 |a DE-11 |a DE-824 |a DE-19 |a DE-706 | ||
| 050 | 0 | |a QA567.2.E44 | |
| 082 | 0 | |a 516.3/52 |2 22 | |
| 084 | |a SI 320 |0 (DE-625)143123: |2 rvk | ||
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a SK 200 |0 (DE-625)143223: |2 rvk | ||
| 084 | |a MAT 143f |2 stub | ||
| 084 | |a MAT 145f |2 stub | ||
| 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 | |
| 650 | 0 | 7 | |a Elliptische Kurve |0 (DE-588)4014487-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Galois-Darstellung |0 (DE-588)4221407-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Elliptische Kurve |0 (DE-588)4014487-2 |D s |
| 689 | 0 | 1 | |a Galois-Darstellung |0 (DE-588)4221407-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a London mathematical society lecture note series |v 356 |w (DE-604)BV000000130 |9 356 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016684353 | ||
Record in the Search Index
| _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 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Delbourgo, Daniel |
| author_facet | Delbourgo, Daniel |
| author_role | aut |
| author_sort | Delbourgo, Daniel |
| author_variant | d d dd |
| building | Verbundindex |
| bvnumber | BV035015173 |
| callnumber-first | Q - Science |
| callnumber-label | QA567 |
| callnumber-raw | QA567.2.E44 |
| callnumber-search | QA567.2.E44 |
| callnumber-sort | QA 3567.2 E44 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 320 SK 180 SK 200 |
| classification_tum | MAT 143f MAT 145f |
| ctrlnum | (OCoLC)227275650 (DE-599)HBZHT015605107 |
| dewey-full | 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01801nam a2200469 cb4500</leader><controlfield tag="001">BV035015173</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20111129 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080821s2008 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521728669</subfield><subfield code="9">978-0-521-72866-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)227275650</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)HBZHT015605107</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA567.2.E44</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.3/52</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 320</subfield><subfield code="0">(DE-625)143123:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 200</subfield><subfield code="0">(DE-625)143223:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 143f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 145f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Delbourgo, Daniel</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Elliptic curves and big Galois representations</subfield><subfield code="c">Daniel Delbourgo</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2008</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 281 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">London mathematical society lecture note series</subfield><subfield code="v">356</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Curves, Elliptic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Galois theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Elliptische Kurve</subfield><subfield code="0">(DE-588)4014487-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Galois-Darstellung</subfield><subfield code="0">(DE-588)4221407-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Elliptische Kurve</subfield><subfield code="0">(DE-588)4014487-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Galois-Darstellung</subfield><subfield code="0">(DE-588)4221407-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">London mathematical society lecture note series</subfield><subfield code="v">356</subfield><subfield code="w">(DE-604)BV000000130</subfield><subfield code="9">356</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016684353</subfield></datafield></record></collection> |
| 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 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016684353 |
| oclc_num | 227275650 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11 DE-824 DE-19 DE-BY-UBM DE-706 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11 DE-824 DE-19 DE-BY-UBM DE-706 |
| physical | IX, 281 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| 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 |
| volume_link | (DE-604)BV000000130 |
| work_keys_str_mv | AT delbourgodaniel ellipticcurvesandbiggaloisrepresentations |