Elliptic Curves over Number Fields with Prescribed Reduction Type:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | German |
| Veröffentlicht: |
Wiesbaden
Vieweg+Teubner Verlag
1983
|
| Schriftenreihe: | Aspects of Mathematics / Aspekte der Mathematik
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Let K be an algebraic number field. The function attaching to each elliptic curve over K its conductor is constant on isoger. y classes of elliptic curves over K (for the definitions see chapter 1). ~Ioreover, for a given ideal a in OK the number of isogeny classes of elliptic curves over K with conductor a is finite. In these notes we deal with the following problem: How can one explicitly construct a set of representatives for the isogeny classes of elliptic curves over K with conductor a for a given ideal a in OK? The conductor of an elliptic curve over K is a numerical invariant which measures, in some sense, the badness of the reduction of the elliptic curve modulo the prime ideals in OK' It plays an important role in the famous Weil-Langlands conjecture on the connection between elliptic curves over K and congruence subgroups in 5L2(OK) • In case K ~ this connection can be stated as follows. For any ideal a = (N) in ~ let ro(N) be the congruence subgroup ro(N) { (: ~) E 5L2 (~) c E (N) } of 5L2 (~) and let 52 (fo (N» be the space of cusp forms of weight 2 for r 0 (N) Now Weil conjectured that there exists a bijection between the rational normalized eigenforms in 52(ro(N» for the Heckealgebra and the - 2 - Lsug~ny classes uf elliptic curves over ~ with conductor a = (N) |
| Beschreibung: | 1 Online-Ressource (213S.) |
| ISBN: | 9783322875990 9783528085698 |
| ISSN: | 0179-2156 |
| DOI: | 10.1007/978-3-322-87599-0 |
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| 245 | 1 | 0 | |a Elliptic Curves over Number Fields with Prescribed Reduction Type |c von Michael Laska |
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| 500 | |a Let K be an algebraic number field. The function attaching to each elliptic curve over K its conductor is constant on isoger. y classes of elliptic curves over K (for the definitions see chapter 1). ~Ioreover, for a given ideal a in OK the number of isogeny classes of elliptic curves over K with conductor a is finite. In these notes we deal with the following problem: How can one explicitly construct a set of representatives for the isogeny classes of elliptic curves over K with conductor a for a given ideal a in OK? The conductor of an elliptic curve over K is a numerical invariant which measures, in some sense, the badness of the reduction of the elliptic curve modulo the prime ideals in OK' It plays an important role in the famous Weil-Langlands conjecture on the connection between elliptic curves over K and congruence subgroups in 5L2(OK) • In case K ~ this connection can be stated as follows. For any ideal a = (N) in ~ let ro(N) be the congruence subgroup ro(N) { (: ~) E 5L2 (~) c E (N) } of 5L2 (~) and let 52 (fo (N» be the space of cusp forms of weight 2 for r 0 (N) Now Weil conjectured that there exists a bijection between the rational normalized eigenforms in 52(ro(N» for the Heckealgebra and the - 2 - Lsug~ny classes uf elliptic curves over ~ with conductor a = (N) | ||
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Datensatz im Suchindex
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| author | Laska, Michael |
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Allgemeine Naturwissenschaft Mathematik |
| doi_str_mv | 10.1007/978-3-322-87599-0 |
| format | Electronic eBook |
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| id | DE-604.BV042444132 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:51Z |
| institution | BVB |
| isbn | 9783322875990 9783528085698 |
| issn | 0179-2156 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027879378 |
| oclc_num | 864067929 |
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| publishDate | 1983 |
| publishDateSearch | 1983 |
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| publisher | Vieweg+Teubner Verlag |
| record_format | marc |
| series2 | Aspects of Mathematics / Aspekte der Mathematik |
| spelling | Laska, Michael Verfasser aut Elliptic Curves over Number Fields with Prescribed Reduction Type von Michael Laska Wiesbaden Vieweg+Teubner Verlag 1983 1 Online-Ressource (213S.) txt rdacontent c rdamedia cr rdacarrier Aspects of Mathematics / Aspekte der Mathematik 0179-2156 Let K be an algebraic number field. The function attaching to each elliptic curve over K its conductor is constant on isoger. y classes of elliptic curves over K (for the definitions see chapter 1). ~Ioreover, for a given ideal a in OK the number of isogeny classes of elliptic curves over K with conductor a is finite. In these notes we deal with the following problem: How can one explicitly construct a set of representatives for the isogeny classes of elliptic curves over K with conductor a for a given ideal a in OK? The conductor of an elliptic curve over K is a numerical invariant which measures, in some sense, the badness of the reduction of the elliptic curve modulo the prime ideals in OK' It plays an important role in the famous Weil-Langlands conjecture on the connection between elliptic curves over K and congruence subgroups in 5L2(OK) • In case K ~ this connection can be stated as follows. For any ideal a = (N) in ~ let ro(N) be the congruence subgroup ro(N) { (: ~) E 5L2 (~) c E (N) } of 5L2 (~) and let 52 (fo (N» be the space of cusp forms of weight 2 for r 0 (N) Now Weil conjectured that there exists a bijection between the rational normalized eigenforms in 52(ro(N» for the Heckealgebra and the - 2 - Lsug~ny classes uf elliptic curves over ~ with conductor a = (N) Mathematics Mathematics, general Mathematik Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Algebraischer Zahlkörper (DE-588)4068537-8 s 1\p DE-604 https://doi.org/10.1007/978-3-322-87599-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Laska, Michael Elliptic Curves over Number Fields with Prescribed Reduction Type Mathematics Mathematics, general Mathematik Elliptische Kurve (DE-588)4014487-2 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd |
| subject_GND | (DE-588)4014487-2 (DE-588)4068537-8 |
| title | Elliptic Curves over Number Fields with Prescribed Reduction Type |
| title_auth | Elliptic Curves over Number Fields with Prescribed Reduction Type |
| title_exact_search | Elliptic Curves over Number Fields with Prescribed Reduction Type |
| title_full | Elliptic Curves over Number Fields with Prescribed Reduction Type von Michael Laska |
| title_fullStr | Elliptic Curves over Number Fields with Prescribed Reduction Type von Michael Laska |
| title_full_unstemmed | Elliptic Curves over Number Fields with Prescribed Reduction Type von Michael Laska |
| title_short | Elliptic Curves over Number Fields with Prescribed Reduction Type |
| title_sort | elliptic curves over number fields with prescribed reduction type |
| topic | Mathematics Mathematics, general Mathematik Elliptische Kurve (DE-588)4014487-2 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Elliptische Kurve Algebraischer Zahlkörper |
| url | https://doi.org/10.1007/978-3-322-87599-0 |
| work_keys_str_mv | AT laskamichael ellipticcurvesovernumberfieldswithprescribedreductiontype |