Typically bounding torsion
Typically bounding torsion
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典型的边界扭转
DOI：
10.1016/j.jnt.2018.04.005
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发表时间：
2017
影响因子：
0.7
通讯作者：
P. Pollack
中科院分区：
文献类型：
--
作者：
P. L. Clark;Marko Milosevic;P. Pollack
我们在数域上定义的阿贝尔簇族上制定了典型的挠率有界性概念。这意味着族中元素的挠率子群可以通过从族中移除在位于任意小密度集中的度数域上定义的所有阿贝尔簇来统一有界。我们表明，对于每个固定 g，挠率通常以全维 CM 阿贝尔簇为界。我们表明，扭转量在所有椭圆曲线族上并不典型有界，并且我们在 j 不变量度固定的椭圆曲线扭转量的典型有界性上建立了结果（一些是无条件的，一些是有条件的）。
We formulate the notion oftypicalboundednessof torsion on a family of abelian varieties defined over number fields. This means that the torsion subgroups of elements in the family can be made uniformly bounded by removing from the family all abelian varieties defined over number fields of degree lying in a set of arbitrarily small density. We show that for each fixedg, torsion is typically bounded on the family of allg-dimensional CM abelian varieties. We show that torsion isnottypically bounded on the family of all elliptic curves, and we establish results – some unconditional and some conditional – on typical boundedness of torsion of elliptic curves for which the degree of thej-invariant is fixed.