[数学] Neron-Severi秩至少K3曲面的Shimura曲线计算 19 [推广有奖]

摘要翻译：
已知Picard数rho(=S的Neron-Severi群的秩）至少为19的K3曲面S用模曲线X参数化，这些模曲线X包括与Q上四元数代数的同余子群相关的各种Shimura模曲线。在这样的K3曲面族中，一个曲面的Rho=20当且仅当它对应于X上的一个CM点。我们用它来计算Shimura曲线的方程、它们之间的自然映射和CM坐标，远远超出了我们在“Shimura曲线计算”(1998)=<http://arxiv.org/abs/math/0005160>中直接处理这些曲线所能做的事情
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英文标题：
《Shimura curve computations via K3 surfaces of Neron-Severi rank at least
  19》
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作者：
Noam D. Elkies
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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：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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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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英文摘要：
  It is known that K3 surfaces S whose Picard number rho (= rank of the Neron-Severi group of S) is at least 19 are parametrized by modular curves X, and these modular curves X include various Shimura modular curves associated with congruence subgroups of quaternion algebras over Q. In a family of such K3 surfaces, a surface has rho=20 if and only if it corresponds to a CM point on X. We use this to compute equations for Shimura curves, natural maps between them, and CM coordinates well beyond what could be done by working with the curves directly as we did in ``Shimura Curve Computations'' (1998) = <http://arxiv.org/abs/math/0005160>
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PDF链接：
https://arxiv.org/pdf/0802.1301