摘要翻译:
本文证明了p-adic L函数的非消失性如何控制具有CM的椭圆曲线中与原点补相关的Selmer变体的维数。作为推论,我们得到了这类曲线的Siegel定理的PI_1证明。
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英文标题:
《p-adic L-functions and Selmer varieties associated to elliptic curves
with complex multiplication》
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作者:
Minhyong Kim
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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: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:
We show how non-vanishing of p-adic L functions controls the dimensions of Selmer varieties associated to the complement of the origin in an elliptic curve with CM. As a corollary, one obtains a \pi_1-proof of the theorem of Siegel for such curves.
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PDF链接:
https://arxiv.org/pdf/0710.5290