On Shimura curves in the Schottky locus
| dc.creator | Kukulies, Stefan | |
| dc.date | 2007-05-30 | |
| dc.date | 2008-04-07 | |
| dc.date.accessioned | 2026-07-07T09:30:18Z | |
| dc.date.available | 2026-07-07T09:30:18Z | |
| dc.description | We show that a given rational Shimura curve Y with strictly maximal Higgs field in the moduli space of g-dimensional abelian varieties does not generically intersect the Schottky locus for large g. We achieve this by using a result of Viehweg and Zuo which says that if Y parameterizes a family of curves of genus g, then the corresponding family of Jacobians is isogenous over Y to the g-fold product of a modular family of elliptic curves. After reducing the situation from the field of complex numbers to a finite field, we will see, combining the Weil and Sato-Tate conjectures, that this is impossible for large genus g. | |
| dc.description | 23 pages, shortened version of my PhD thesis | |
| dc.identifier | https://arxiv.org/abs/0705.4432 | |
| dc.identifier | http://arxiv.org/abs/0705.4432 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158081 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14D05, 14H40, 14G35 | |
| dc.title | On Shimura curves in the Schottky locus | |
| dc.type | text |