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