Elementary modular Iwasawa theory:
"This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2021
|
| Schriftenreihe: | Series on number theory and its applications
vol. 16 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author's 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry. Starting with a description of Iwasawa's classical results on his proof of the main conjecture under the Kummer-Vandiver conjecture (which proves cyclicity of his Iwasawa module more than just proving his main conjecture), we describe a generalization of the method proving cyclicity to the adjoint Selmer group of every ordinary deformation of a two-dimensional Artin Galois representation. The fundamentals in the first five chapters are as follows: Iwasawa's proof; a modular version of Iwasawa's discovery by Kubert-Lang as an introduction to modular forms; a level-headed description of the p-adic interpolation of modular forms and p-adic L-functions, which are developed into a modular deformation theory; Galois deformation theory of the abelian case. The continuing chapters provide the level of exposition accessible to graduate students, while the results are the latest"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | 1 Online-Ressource (448 Seiten) |
| ISBN: | 9789811241376 9811241376 |
| DOI: | 10.1142/12398 |
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Datensatz im Suchindex
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/4 |
| dewey-search | 512.7/4 |
| dewey-sort | 3512.7 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1142/12398 |
| format | Electronic eBook |
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| id | DE-604.BV047627784 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:44:42Z |
| indexdate | 2024-07-10T09:17:37Z |
| institution | BVB |
| isbn | 9789811241376 9811241376 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033012258 |
| oclc_num | 1289770690 |
| open_access_boolean | |
| physical | 1 Online-Ressource (448 Seiten) |
| psigel | ZDB-124-WOP |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | World Scientific |
| record_format | marc |
| series2 | Series on number theory and its applications |
| spelling | Hida, Haruzo Verfasser aut Elementary modular Iwasawa theory Haruzo Hida Singapore World Scientific 2021 1 Online-Ressource (448 Seiten) txt rdacontent c rdamedia cr rdacarrier Series on number theory and its applications vol. 16 Includes bibliographical references and index "This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author's 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry. Starting with a description of Iwasawa's classical results on his proof of the main conjecture under the Kummer-Vandiver conjecture (which proves cyclicity of his Iwasawa module more than just proving his main conjecture), we describe a generalization of the method proving cyclicity to the adjoint Selmer group of every ordinary deformation of a two-dimensional Artin Galois representation. The fundamentals in the first five chapters are as follows: Iwasawa's proof; a modular version of Iwasawa's discovery by Kubert-Lang as an introduction to modular forms; a level-headed description of the p-adic interpolation of modular forms and p-adic L-functions, which are developed into a modular deformation theory; Galois deformation theory of the abelian case. The continuing chapters provide the level of exposition accessible to graduate students, while the results are the latest"-- Iwasawa theory Galois theory Modules (Algebra) Iwasawa-Theorie (DE-588)4384573-3 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Electronic books Galois-Theorie (DE-588)4155901-0 s Iwasawa-Theorie (DE-588)4384573-3 s DE-604 Erscheint auch als Druck-Ausgabe 9789811241369 Erscheint auch als Druck-Ausgabe 9811241368 https://doi.org/10.1142/12398 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Hida, Haruzo Elementary modular Iwasawa theory Iwasawa theory Galois theory Modules (Algebra) Iwasawa-Theorie (DE-588)4384573-3 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| subject_GND | (DE-588)4384573-3 (DE-588)4155901-0 |
| title | Elementary modular Iwasawa theory |
| title_auth | Elementary modular Iwasawa theory |
| title_exact_search | Elementary modular Iwasawa theory |
| title_exact_search_txtP | Elementary modular Iwasawa theory |
| title_full | Elementary modular Iwasawa theory Haruzo Hida |
| title_fullStr | Elementary modular Iwasawa theory Haruzo Hida |
| title_full_unstemmed | Elementary modular Iwasawa theory Haruzo Hida |
| title_short | Elementary modular Iwasawa theory |
| title_sort | elementary modular iwasawa theory |
| topic | Iwasawa theory Galois theory Modules (Algebra) Iwasawa-Theorie (DE-588)4384573-3 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| topic_facet | Iwasawa theory Galois theory Modules (Algebra) Iwasawa-Theorie Galois-Theorie |
| url | https://doi.org/10.1142/12398 |
| work_keys_str_mv | AT hidaharuzo elementarymodulariwasawatheory |