Iwasawa theory, projective modules, and modular representations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2011
|
| Series: | Memoirs of the American Mathematical Society
992 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 211, Number 992 (second of 5 numbers) |
| Physical Description: | IV, 185 S. |
| ISBN: | 9780821849316 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Iwasawa theory, projective modules, and modular representations
Autor: Greenberg, Ralph
Jahr: 2011
Contents
Chapter 1. Introduction. 1
1.1. Congruence relations. 2
1.2. Selmer groups for elliptic curves. 6
1.3. Behavior of Iwasawa invariants. 9
1.4. Selmer atoms. 10
1.5. Parity questions. 12
1.6. Other situations. 14
1.7. Organization and acknowledgements. 16
Chapter 2. Projective and quasi-projective modules. 17
2.1. Criteria for projectivity and quasi-projectivity. 17
2.2. Nonzero ^-invariant. 24
2.3. The structure of AG/AG0. 26
2.4. Projective dimension. 27
Chapter 3. Projectivity or quasi-projectivity of Xg0 (-¦-__). 31
3.1. The proof of Theorem 1. 31
3.2. Quasi-projectivity. 37
3.3. Partial converses. 39
3.4. More general situations. 41
3.5. A i T-extensions. 44
Chapter 4. Selmer atoms. 47
4.1. Various cohomology groups. Coranks. Criteria for vanishing. 47
4.2. Selmer groups for E p] ® a. 56
4.3. Justification of (1.4.b) and (1.4.c). 59
4.4. Justification of (1.4.d) and the proof of Theorem 2. 62
4.5. Finiteness of Selmer atoms. 63
Chapter 5. The structure of ?{.(____, E). 69
5.1. Determination of _£,,(_-). 70
5.2. Determination of (pe,v,x)- 72
5.3. Projectivity and Herbrand quotients. 74
Chapter 6. The case where A is a p-group. 77
Chapter 7. Other specific groups. 81
7.1. The groups A4, S4, and S5.
7.2. The group PGL_(FP).
7.3. The groups PGL2{Z/pr+1Z) for r 1.
7.4. Extensions of (Z/pZ)x by a p-group.
81
84
90
96
iv CONTENTS
Chapter 8. Some arithmetic illustrations. 105
8.1. An illustration where 5_0 is empty. 105
8.2. An illustration where S0 is non-empty. 109
8.3. An illustration where the ass,s have abelian image. 114
8.4. False Täte extensions of Q. 127
Chapter 9. Self-dual representations. 131
9.1. Various classes of groups. 131
9.2. nfi groups. 133
9.3. Some parity results concerning multiplicities. 137
9.4. Self-dual representations and the decomposition map. 139
Chapter 10. A duality theorem. 141
10.1. The main result. 142
10.2. Consequences concerning the parity of se(p). 145
Chapter 11. p-modular functions. 151
11.1. Basic examples of p-modular functions. 151
11.2. Some p-modular functions involving multiplicities. 152
Chapter 12. Parity. 159
12.1. The proof of Theorem 3. 160
12.2. Consequences concerning WDel(E,p) and WSelp(E,p). 167
Chapter 13. More arithmetic illustrations. 169
13.1. An illustration where ^eD^k/f is empty. 170
13.2. An illustration where K C Q{E p°°}). 172
13.3. An illustration where Gal(.f_/Q) is isomorphic to Bn or Hn. 174
Bibliography 183
|
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| id | DE-604.BV037396519 |
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| indexdate | 2024-07-09T23:23:25Z |
| institution | BVB |
| isbn | 9780821849316 |
| language | English |
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| physical | IV, 185 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | American Math. Soc. |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Greenberg, Ralph 1944- Verfasser (DE-588)1011412357 aut Iwasawa theory, projective modules, and modular representations Ralph Greenberg Providence, RI American Math. Soc. 2011 IV, 185 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 992 Volume 211, Number 992 (second of 5 numbers) Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Iwasawa-Theorie (DE-588)4384573-3 gnd rswk-swf Iwasawa-Theorie (DE-588)4384573-3 s Elliptische Kurve (DE-588)4014487-2 s DE-604 Memoirs of the American Mathematical Society 992 (DE-604)BV008000141 992 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022549304&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Greenberg, Ralph 1944- Iwasawa theory, projective modules, and modular representations Memoirs of the American Mathematical Society Elliptische Kurve (DE-588)4014487-2 gnd Iwasawa-Theorie (DE-588)4384573-3 gnd |
| subject_GND | (DE-588)4014487-2 (DE-588)4384573-3 |
| title | Iwasawa theory, projective modules, and modular representations |
| title_auth | Iwasawa theory, projective modules, and modular representations |
| title_exact_search | Iwasawa theory, projective modules, and modular representations |
| title_full | Iwasawa theory, projective modules, and modular representations Ralph Greenberg |
| title_fullStr | Iwasawa theory, projective modules, and modular representations Ralph Greenberg |
| title_full_unstemmed | Iwasawa theory, projective modules, and modular representations Ralph Greenberg |
| title_short | Iwasawa theory, projective modules, and modular representations |
| title_sort | iwasawa theory projective modules and modular representations |
| topic | Elliptische Kurve (DE-588)4014487-2 gnd Iwasawa-Theorie (DE-588)4384573-3 gnd |
| topic_facet | Elliptische Kurve Iwasawa-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022549304&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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