Relative Manin–Mumford in additive extensions
Relative Manin–Mumford in additive extensions
复制标题
加法扩展中的相对 Manin-Mumford
DOI：
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发表时间：
2018
影响因子：
1.3
通讯作者：
Harry Schmidt
中科院分区：
文献类型：
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作者：
Harry Schmidt
在最近的论文中，Masser和Zannier证明了各种阿贝尔变种族的“相对Manin-Mumford”型的各种结果，其中一些的定义域限制在代数数上。一般来说，这意味着曲线上的扭转点的集合是有限的。在Bertrand， Masser和Zannier发现椭圆族的乘法扩展的一些令人惊讶的反例之后，三位作者与Pillay一起在代数数上完全解决了这种情况。这里我们处理曲面的最后一种情况，即椭圆族的加性扩展，甚至在所有复数的域上。特别地，不存在类似的反例。多项式环上的Pell方程和初等项的积分有有限的结果。我们的工作可以变得有效（与之前的大多数相反），主要是因为我们只对分析曲线使用计数结果。
In recent papers Masser and Zannier have proved various results of “relative Manin–Mumford” type for various families of abelian varieties, some with field of definition restricted to the algebraic numbers. Typically these imply the finiteness of the set of torsion points on a curve in the family. After Bertrand, Masser, and Zannier discovered some surprising counterexamples for multiplicative extensions of elliptic families, the three authors together with Pillay settled completely the situation for this case over the algebraic numbers. Here we treat the last remaining case of surfaces, that of additive extensions of elliptic families, and even over the field of all complex numbers. In particular analogous counterexamples do not exist. There are finiteness consequences for Pell’s equation over polynomial rings and integration in elementary terms. Our work can be made effective (as opposed to most of that preceding), mainly because we use counting results only for analytic curves.
简单阿贝尔曲面族上的扭点和多项式环上的佩尔方程（附有 E. V. Flynn 的附录）
影响因子：
2.6
作者：
Masser D
通讯作者：
Masser D