Geometric modular forms and elliptic curves:
This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addi...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2012
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| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction. In this new second edition, a detailed description of Barsotti-Tate groups (including formal Lie groups) is added to Chapter 1. As an application, a down-to-earth description of formal deformation theory of elliptic curves is incorporated at the end of Chapter 2 (in order to make the proof of regularity of the moduli of elliptic curve more conceptual), and in Chapter 4, though limited to ordinary cases, newly incorporated are Ribet's theorem of full image of modular p-adic Galois representation and its generalization to 'big' [symbol]-adic Galois representations under mild assumptions (a new result of the author). Though some of the striking developments described above is out of the scope of this introductory book, the author gives a taste of present day research in the area of Number Theory at the very end of the book (giving a good account of modularity theory of abelian Q-varieties and Q-curves) |
| Beschreibung: | xiii, 454 p |
| ISBN: | 9789814368650 |
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| 520 | |a This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction. In this new second edition, a detailed description of Barsotti-Tate groups (including formal Lie groups) is added to Chapter 1. As an application, a down-to-earth description of formal deformation theory of elliptic curves is incorporated at the end of Chapter 2 (in order to make the proof of regularity of the moduli of elliptic curve more conceptual), and in Chapter 4, though limited to ordinary cases, newly incorporated are Ribet's theorem of full image of modular p-adic Galois representation and its generalization to 'big' [symbol]-adic Galois representations under mild assumptions (a new result of the author). Though some of the striking developments described above is out of the scope of this introductory book, the author gives a taste of present day research in the area of Number Theory at the very end of the book (giving a good account of modularity theory of abelian Q-varieties and Q-curves) | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Hida, Haruzo |
| author_facet | Hida, Haruzo |
| author_role | aut |
| author_sort | Hida, Haruzo |
| author_variant | h h hh |
| building | Verbundindex |
| bvnumber | BV044638773 |
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| ctrlnum | (ZDB-124-WOP)00002604 (OCoLC)1005228971 (DE-599)BVBBV044638773 |
| dewey-full | 516.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.352 |
| dewey-search | 516.352 |
| dewey-sort | 3516.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044638773 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:54Z |
| institution | BVB |
| isbn | 9789814368650 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030036745 |
| oclc_num | 1005228971 |
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| owner | DE-92 |
| owner_facet | DE-92 |
| physical | xiii, 454 p |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| spelling | Hida, Haruzo Verfasser aut Geometric modular forms and elliptic curves Haruzo Hida Singapore World Scientific Pub. Co. c2012 xiii, 454 p txt rdacontent c rdamedia cr rdacarrier This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction. In this new second edition, a detailed description of Barsotti-Tate groups (including formal Lie groups) is added to Chapter 1. As an application, a down-to-earth description of formal deformation theory of elliptic curves is incorporated at the end of Chapter 2 (in order to make the proof of regularity of the moduli of elliptic curve more conceptual), and in Chapter 4, though limited to ordinary cases, newly incorporated are Ribet's theorem of full image of modular p-adic Galois representation and its generalization to 'big' [symbol]-adic Galois representations under mild assumptions (a new result of the author). Though some of the striking developments described above is out of the scope of this introductory book, the author gives a taste of present day research in the area of Number Theory at the very end of the book (giving a good account of modularity theory of abelian Q-varieties and Q-curves) Curves, Elliptic Forms, Modular Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Modulraum (DE-588)4183462-8 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Modulraum (DE-588)4183462-8 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 9789814368643 (hbk.) Erscheint auch als Druck-Ausgabe 9814368644 (hbk.) http://www.worldscientific.com/worldscibooks/10.1142/8277#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hida, Haruzo Geometric modular forms and elliptic curves Curves, Elliptic Forms, Modular Elliptische Kurve (DE-588)4014487-2 gnd Modulraum (DE-588)4183462-8 gnd |
| subject_GND | (DE-588)4014487-2 (DE-588)4183462-8 |
| title | Geometric modular forms and elliptic curves |
| title_auth | Geometric modular forms and elliptic curves |
| title_exact_search | Geometric modular forms and elliptic curves |
| title_full | Geometric modular forms and elliptic curves Haruzo Hida |
| title_fullStr | Geometric modular forms and elliptic curves Haruzo Hida |
| title_full_unstemmed | Geometric modular forms and elliptic curves Haruzo Hida |
| title_short | Geometric modular forms and elliptic curves |
| title_sort | geometric modular forms and elliptic curves |
| topic | Curves, Elliptic Forms, Modular Elliptische Kurve (DE-588)4014487-2 gnd Modulraum (DE-588)4183462-8 gnd |
| topic_facet | Curves, Elliptic Forms, Modular Elliptische Kurve Modulraum |
| url | http://www.worldscientific.com/worldscibooks/10.1142/8277#t=toc |
| work_keys_str_mv | AT hidaharuzo geometricmodularformsandellipticcurves |