On the p-adic closure of a subgroup of rational points on an Abelian variety
On the p-adic closure of a subgroup of rational points on an Abelian variety
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关于阿贝尔簇上有理点子群的 p 进闭
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Waldschmidt
中科院分区：
文献类型：
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作者：
M. Waldschmidt
2007 年，Poonen（未发表）研究了交换代数群上有理点子群的 p-adic 闭包。最近，贝莱什针对阿贝尔簇的特殊情况提出了同样的问题。这些问题是 Mazur 之前提出的有关真实拓扑有理点密度问题的 p-adic 类似物。对于有理数域上的简单阿贝尔簇，我们证明实际的 p 进阶至少是期望值的三分之一。
In 2007, Poonen (unpublished) studied the p-adic closure of a subgroup of rational points on a commutative algebraic group. More recently, Bellaïche asked the same question for the special case of Abelian varieties. These problems are p-adic analogues of a question raised earlier by Mazur on the density of rational points for the real topology. For a simple Abelian variety over the field of rational numbers, we show that the actual p-adic rank is at least the third of the expected value.
影响因子：
1
作者：
Ghosh A
通讯作者：
Ghosh A