Runge's method and modular curves
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BILU, Yuri | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PARENT, Pierre | |
| dc.date.accessioned | 2024-04-04T02:18:49Z | |
| dc.date.available | 2024-04-04T02:18:49Z | |
| dc.date.issued | 2011 | |
| dc.identifier.issn | 1073-7928 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189349 | |
| dc.description.abstractEn | We bound the j-invariant of S-integral points on arbitrary modular curves over arbitrary number fields, in terms of the congruence group defining the curve, assuming a certain Runge condition is satisfied by our objects. We then apply our bounds to prove that for sufficiently large prime p, the points of X-0(+) (p(r))(Q) with r > 1 are either cusps or complex multiplication points. This can be interpreted as the non-existence of quadratic elliptic Q-curves with higher prime-power degree. | |
| dc.language.iso | en | |
| dc.publisher | Oxford University Press (OUP) | |
| dc.title.en | Runge's method and modular curves | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1093/imrn/rnq141 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 0907.3306 | |
| bordeaux.journal | International Mathematics Research Notices | |
| bordeaux.page | 1997-2027 | |
| bordeaux.volume | 9 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00960239 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00960239v1 | |
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