On Shimura curves in the Schottky locus

dc.creatorKukulies, Stefan
dc.date2007-05-30
dc.date2008-04-07
dc.date.accessioned2026-07-07T09:30:18Z
dc.date.available2026-07-07T09:30:18Z
dc.descriptionWe 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.description23 pages, shortened version of my PhD thesis
dc.identifierhttps://arxiv.org/abs/0705.4432
dc.identifierhttp://arxiv.org/abs/0705.4432
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158081
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subject14D05, 14H40, 14G35
dc.titleOn Shimura curves in the Schottky locus
dc.typetext

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