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Genus two curves with quaternionic multiplication and modular jacobian
| dc.contributor.author | González i Rovira, Josep |
| dc.contributor.author | Guàrdia Rubies, Jordi |
| dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
| dc.date.accessioned | 2008-04-23T16:48:16Z |
| dc.date.available | 2008-04-23T16:48:16Z |
| dc.date.issued | 2007 |
| dc.identifier.citation | González i Rovira, J.; Guàrdia Rubies, J. Genus two curves with quaternionic multiplication and modular jacobian. "Mathematics of computation", 2007, vol. 78, núm. 265, p. 575-589. |
| dc.identifier.uri | http://hdl.handle.net/2117/1958 |
| dc.description.abstract | We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces $A_f$ with quaternionic multiplication attached to a normalized newform $f$ without complex multiplication. We include an example of $A_f$ with quaternionic multiplication for which we find numerically a curve $C$ whose Jacobian is $A_f$ up to numerical approximation, and we prove that it has quaternionic multiplication and is isogenous to $A_f$. |
| dc.format.extent | 15 p. |
| dc.language.iso | eng |
| dc.rights | Attribution-NonCommercial-NoDerivs 2.5 Spain |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
| dc.subject.lcsh | Quaternions |
| dc.subject.lcsh | Modular curves |
| dc.subject.lcsh | Abelian varieties |
| dc.subject.other | Genus two curves |
| dc.subject.other | Quaternionic multiplication |
| dc.subject.other | Modular abelian surfaces |
| dc.title | Genus two curves with quaternionic multiplication and modular jacobian |
| dc.type | Article |
| dc.subject.lemac | Quaternions |
| dc.subject.lemac | Corbes modulars |
| dc.subject.lemac | Varietats abelianes |
| dc.contributor.group | Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
| dc.subject.ams | Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) |
| dc.subject.ams | Classificació AMS::14 Algebraic geometry::14H Curves |
| dc.rights.access | Open Access |
| local.identifier.drac | 1231237 |
| dc.relation.projectidctt | MTM2006-15038-C02-02. |
| local.citation.publicationName | Mathematics of computation |
| local.citation.volume | 78 |
| local.citation.number | 265 |
| local.citation.startingPage | 575 |
| local.citation.endingPage | 589 |
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