Euler systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton Univ. Press
2000
|
| Schriftenreihe: | Annals of mathematics studies
number 147 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xi, 227 Seiten Diagramme |
| ISBN: | 0691050767 0691050759 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV013249923 | ||
| 003 | DE-604 | ||
| 005 | 20241209 | ||
| 007 | t| | ||
| 008 | 000713s2000 xx |||| |||| 00||| eng d | ||
| 020 | |a 0691050767 |c paperback |9 0-6910-5076-7 | ||
| 020 | |a 0691050759 |c hardcover |9 0-6910-5075-9 | ||
| 035 | |a (OCoLC)44392822 | ||
| 035 | |a (DE-599)BVBBV013249923 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-19 |a DE-20 |a DE-384 |a DE-703 |a DE-824 |a DE-11 |a DE-706 | ||
| 050 | 0 | |a QA247 | |
| 082 | 0 | |a 512/.74 |2 21 | |
| 084 | |a SI 830 |0 (DE-625)143195: |2 rvk | ||
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 100 | 1 | |a Rubin, Karl |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Euler systems |c by Karl Rubin |
| 264 | 1 | |a Princeton, NJ |b Princeton Univ. Press |c 2000 | |
| 264 | 4 | |c © 2000 | |
| 300 | |a xi, 227 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Annals of mathematics studies |v number 147 | |
| 490 | 0 | |a Hermann Weyl lectures | |
| 650 | 7 | |a Algebraïsche meetkunde |2 gtt | |
| 650 | 7 | |a Discontinue groepen |2 gtt | |
| 650 | 7 | |a Getaltheorie |2 gtt | |
| 650 | 4 | |a Nombres algébriques, Théorie des | |
| 650 | 7 | |a Nombres algébriques, Théorie des |2 ram | |
| 650 | 4 | |a Nombres p-adiques | |
| 650 | 7 | |a Nombres p-adiques |2 ram | |
| 650 | 7 | |a P-adische getallen |2 gtt | |
| 650 | 4 | |a Algebraic number theory | |
| 650 | 4 | |a p-adic numbers | |
| 650 | 0 | 7 | |a Kreiskörper |0 (DE-588)4165607-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a p-adische L-Funktion |0 (DE-588)4398270-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elliptische Kurve |0 (DE-588)4014487-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Galois-Kohomologie |0 (DE-588)4019172-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a p-adische L-Funktion |0 (DE-588)4398270-0 |D s |
| 689 | 0 | 1 | |a Galois-Kohomologie |0 (DE-588)4019172-2 |D s |
| 689 | 0 | 2 | |a Kreiskörper |0 (DE-588)4165607-6 |D s |
| 689 | 0 | 3 | |a Elliptische Kurve |0 (DE-588)4014487-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Elektronische Reproduktion |d 2014 |z 9781400865208 |
| 830 | 0 | |a Annals of mathematics studies |v number 147 |w (DE-604)BV000000991 |9 147 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009030438&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009030438 | |
Datensatz im Suchindex
| _version_ | 1817953089302298624 |
|---|---|
| adam_text |
Contents
Acknowledgments xi
Introduction 3
Notation 6
Chapter 1. Galois Cohomology of p adic Representations 9
1.1. p adic Representations 9
1.2. Galois Cohomology 11
1.3. Local Cohomology Groups 12
1.4. Local Duality 18
1.5. Global Cohomology Groups 21
1.6. Examples of Selmer Groups 23
1.7. Global Duality 28
Chapter 2. Euler Systems: Definition and Main Results 33
2.1. Euler Systems 33
2.2. Results over K 36
2.3. Results over K^ 40
2.4. Twisting by Characters of Finite Order 43
Chapter 3. Examples and Applications 47
3.1. Preliminaries 47
3.2. Cyclotomic Units 48
3.3. Elliptic Units 55
3.4. Stickelberger Elements 55
3.5. Elliptic Curves 63
3.6. Symmetric Square of an Elliptic Curve 73
Chapter 4. Derived Cohomology Classes 75
4.1. Setup 75
4.2. The Universal Euler System 78
4.3. Properties of the Universal Euler System 80
4.4. Kolyvagin's Derivative Construction 83
vii
viii CONTENTS
4.5. Local Properties of the Derivative Classes 90
4.6. Local Behavior at Primes Not Dividing pr 92
4.7. Local Behavior at Primes Dividing r 98
4.8. The Congruence 102
Chapter 5. Bounding the Selmer Group 105
5.1. Preliminaries 105
5.2. Bounding the Order of the Selmer Group 106
5.3. Bounding the Exponent of the Selmer Group 114
Chapter 6. Twisting 119
6.1. Twisting Representations 119
6.2. Twisting Cohomology Groups 121
6.3. Twisting Euler Systems 122
6.4. Twisting Theorems 125
6.5. Examples and Applications 125
Chapter 7. Iwasawa Theory 129
7.1. Overview 129
7.2. Galois Groups and the Evaluation Map 135
7.3. Proof of Theorem 2.3.2 141
7.4. The Kernel and Cokernel of the Restriction Map 145
7.5. Galois Equivariance of the Evaluation Maps 147
7.6. Proof of Proposition 7.1.7 151
7.7. Proof of Proposition 7.1.9 154
Chapter 8. Euler Systems and p adic L functions 163
8.1. The Setting 164
8.2. Perrin Riou's p adic L function and Related Conjectures 166
8.3. Connection with Euler Systems when oL = 1 168
8.4. Example: Cyclotomic Units 171
8.5. Connection with Euler Systems when d_ 1 173
Chapter 9. Variants 175
9.1. Rigidity 175
9.2. Finite Primes Splitting Completely in K^/K 178
9.3. Euler Systems of Finite Depth 179
9.4. Anticyclotomic Euler Systems 180
9.5. Additional Local Conditions 183
9.6. Varying the Euler Factors 185
Appendix A. Linear Algebra 189
CONTENTS ix
A.I. Herbrand Quotients 189
A.2. p adic Representations 191
Appendix B. Continuous Cohomology and Inverse Limits 195
B.I. Preliminaries 195
B.2. Continuous Cohomology 195
B.3. Inverse Limits 198
B.4. Induced Modules 201
B.5. Semilocal Galois Cohomology 202
Appendix C. Cohomology of p adic Analytic Groups 205
C.I. Irreducible Actions of Compact Groups 205
C.2. Application to Galois Representations 207
Appendix D. p adic Calculations in Cyclotomic Fields 211
D.I. Local Units in Cyclotomic Fields 211
D.2. Cyclotomic Units 216
Bibliography 219
Index of Symbols 223
Subject Index 227 |
| any_adam_object | 1 |
| author | Rubin, Karl |
| author_facet | Rubin, Karl |
| author_role | aut |
| author_sort | Rubin, Karl |
| author_variant | k r kr |
| building | Verbundindex |
| bvnumber | BV013249923 |
| callnumber-first | Q - Science |
| callnumber-label | QA247 |
| callnumber-raw | QA247 |
| callnumber-search | QA247 |
| callnumber-sort | QA 3247 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 830 SK 180 |
| ctrlnum | (OCoLC)44392822 (DE-599)BVBBV013249923 |
| dewey-full | 512/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74 |
| dewey-search | 512/.74 |
| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV013249923</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20241209</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">000713s2000 xx |||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0691050767</subfield><subfield code="c">paperback</subfield><subfield code="9">0-6910-5076-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0691050759</subfield><subfield code="c">hardcover</subfield><subfield code="9">0-6910-5075-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)44392822</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013249923</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-706</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA247</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.74</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 830</subfield><subfield code="0">(DE-625)143195:</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="100" ind1="1" ind2=" "><subfield code="a">Rubin, Karl</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Euler systems</subfield><subfield code="c">by Karl Rubin</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ</subfield><subfield code="b">Princeton Univ. Press</subfield><subfield code="c">2000</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2000</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xi, 227 Seiten</subfield><subfield code="b">Diagramme</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">Annals of mathematics studies</subfield><subfield code="v">number 147</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Hermann Weyl lectures</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Algebraïsche meetkunde</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Discontinue groepen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Getaltheorie</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nombres algébriques, Théorie des</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Nombres algébriques, Théorie des</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nombres p-adiques</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Nombres p-adiques</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">P-adische getallen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic number theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">p-adic numbers</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kreiskörper</subfield><subfield code="0">(DE-588)4165607-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">p-adische L-Funktion</subfield><subfield code="0">(DE-588)4398270-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</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-Kohomologie</subfield><subfield code="0">(DE-588)4019172-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">p-adische L-Funktion</subfield><subfield code="0">(DE-588)4398270-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Galois-Kohomologie</subfield><subfield code="0">(DE-588)4019172-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Kreiskörper</subfield><subfield code="0">(DE-588)4165607-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><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=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Elektronische Reproduktion</subfield><subfield code="d">2014</subfield><subfield code="z">9781400865208</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Annals of mathematics studies</subfield><subfield code="v">number 147</subfield><subfield code="w">(DE-604)BV000000991</subfield><subfield code="9">147</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=009030438&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009030438</subfield></datafield></record></collection> |
| id | DE-604.BV013249923 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-09T09:06:09Z |
| institution | BVB |
| isbn | 0691050767 0691050759 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009030438 |
| oclc_num | 44392822 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-20 DE-384 DE-703 DE-824 DE-11 DE-706 |
| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-20 DE-384 DE-703 DE-824 DE-11 DE-706 |
| physical | xi, 227 Seiten Diagramme |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies Hermann Weyl lectures |
| spelling | Rubin, Karl Verfasser aut Euler systems by Karl Rubin Princeton, NJ Princeton Univ. Press 2000 © 2000 xi, 227 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies number 147 Hermann Weyl lectures Algebraïsche meetkunde gtt Discontinue groepen gtt Getaltheorie gtt Nombres algébriques, Théorie des Nombres algébriques, Théorie des ram Nombres p-adiques Nombres p-adiques ram P-adische getallen gtt Algebraic number theory p-adic numbers Kreiskörper (DE-588)4165607-6 gnd rswk-swf p-adische L-Funktion (DE-588)4398270-0 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Galois-Kohomologie (DE-588)4019172-2 gnd rswk-swf p-adische L-Funktion (DE-588)4398270-0 s Galois-Kohomologie (DE-588)4019172-2 s Kreiskörper (DE-588)4165607-6 s Elliptische Kurve (DE-588)4014487-2 s DE-604 Elektronische Reproduktion 2014 9781400865208 Annals of mathematics studies number 147 (DE-604)BV000000991 147 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009030438&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rubin, Karl Euler systems Annals of mathematics studies Algebraïsche meetkunde gtt Discontinue groepen gtt Getaltheorie gtt Nombres algébriques, Théorie des Nombres algébriques, Théorie des ram Nombres p-adiques Nombres p-adiques ram P-adische getallen gtt Algebraic number theory p-adic numbers Kreiskörper (DE-588)4165607-6 gnd p-adische L-Funktion (DE-588)4398270-0 gnd Elliptische Kurve (DE-588)4014487-2 gnd Galois-Kohomologie (DE-588)4019172-2 gnd |
| subject_GND | (DE-588)4165607-6 (DE-588)4398270-0 (DE-588)4014487-2 (DE-588)4019172-2 |
| title | Euler systems |
| title_auth | Euler systems |
| title_exact_search | Euler systems |
| title_full | Euler systems by Karl Rubin |
| title_fullStr | Euler systems by Karl Rubin |
| title_full_unstemmed | Euler systems by Karl Rubin |
| title_short | Euler systems |
| title_sort | euler systems |
| topic | Algebraïsche meetkunde gtt Discontinue groepen gtt Getaltheorie gtt Nombres algébriques, Théorie des Nombres algébriques, Théorie des ram Nombres p-adiques Nombres p-adiques ram P-adische getallen gtt Algebraic number theory p-adic numbers Kreiskörper (DE-588)4165607-6 gnd p-adische L-Funktion (DE-588)4398270-0 gnd Elliptische Kurve (DE-588)4014487-2 gnd Galois-Kohomologie (DE-588)4019172-2 gnd |
| topic_facet | Algebraïsche meetkunde Discontinue groepen Getaltheorie Nombres algébriques, Théorie des Nombres p-adiques P-adische getallen Algebraic number theory p-adic numbers Kreiskörper p-adische L-Funktion Elliptische Kurve Galois-Kohomologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009030438&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000991 |
| work_keys_str_mv | AT rubinkarl eulersystems |