$\cal{D}$ -椭圆层模曲线的局部丢番图性质
Local diophantine properties of modular curves of $\cal{D}$-elliptic sheaves
摘要：
研究了局部域上$\cal{D}$ -椭圆层的模曲线上有理点的存在性及其特殊纤维的结构.讨论了它的一些应用，包括寻找由四元数代数产生的算术群的表示，寻找$\cal{D}$ -椭圆层的模曲线的方程，以及构造违反Hasse原理的曲线.
英文摘要：
We study the existence of rational points on modular curves of $\cal{D}$-elliptic sheaves over local fields and the structure of special fibres of these curves. We discuss some applications which include finding presentations for arithmetic groups arising from quaternion algebras, finding the equations of modular curves of $\cal{D}$-elliptic sheaves, and constructing curves violating the Hasse principle.
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