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摘要翻译：
我们证明了在G维阿贝尔变体模空间中具有严格极大Higgs场的有理Shimura曲线Y不与大G的Schottky轨迹通有相交。我们通过使用Viehweg和Zuo的一个结果来实现这一点，该结果说，如果Y使g属的一族曲线参数化，则相应的Jacobians族在Y上与模椭圆曲线族的g-折积是等价的。在把情况从复数域减少到有限域之后，结合Weil和Sato-Tate的猜想，我们将看到这对于大亏格G是不可能的。
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英文标题：
《On Shimura curves in the Schottky locus》
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作者：
Stefan Kukulies
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/0705.4432
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