摘要翻译：
如果E是奇特征整体函数域F上的非等平凡椭圆曲线，我们证明了E的某些Mordell-Weil群具有相对于固定复环类特征的一维本征空间，条件是适当的Drinfeld-Heegner点在本征空间上的投影是非零。这是Bertolini和Darmon关于有理椭圆曲线的一个定理在函数场设置中的类似，同时也是Brown在Heegner模专著中所证明的主要结果的推广。与数场的情形一样，我们的证明采用了Kolyvagin型变元，上同调机制是由Igusa的经典结果在正特性中提供的对E的扭转的Galois结构的控制启动的。
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英文标题：
《On ring class eigenspaces of Mordell-Weil groups of elliptic curves over
  global function fields》
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作者：
S. Vigni
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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：
  If E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional eigenspace relative to a fixed complex ring class character provided that the projection onto this eigenspace of a suitable Drinfeld-Heegner point is nonzero. This represents the analogue in the function field setting of a theorem for rational elliptic curves due to Bertolini and Darmon, and at the same time is a generalization of the main result proved by Brown in his monograph on Heegner modules. As in the number field case, our proof employs Kolyvagin-type arguments, and the cohomological machinery is started up by the control on the Galois structure of the torsion of E provided by classical results of Igusa in positive characteristic.
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PDF链接：
https://arxiv.org/pdf/0804.1658