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摘要翻译：
描述了定义在单群为非算术Fuchsian群的数域上的秩2的全局幂零微分算子。我们证明了这些微分算子有一个S-积分解。这些微分算子与属2中的Teichmueller曲线自然相关联。它们是Chudnovsky的猜想的反例--Chudnovsky和Dwork。我们还确定了亏格2中本原Teichmueller曲线的模域，并在某些情况下给出了一个显式方程。
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英文标题：
《Differential equations associated with nonarithmetic Fuchsian groups》
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作者：
Irene Bouw, Martin Moeller
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最新提交年份：
2007
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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 describe globally nilpotent differential operators of rank 2 defined over a number field whose monodromy group is a nonarithmetic Fuchsian group. We show that these differential operators have an S-integral solution. These differential operators are naturally associated with Teichmueller curves in genus 2. They are counterexamples to conjectures by Chudnovsky--Chudnovsky and Dwork. We also determine the field of moduli of primitive Teichmueller curves in genus 2, and an explicit equation in some cases.
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PDF链接：
https://arxiv.org/pdf/0710.5277
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