Let A be a non-zero abelian variety defined over a number field K and let (K) over bar be a fixed algebraic closure of K. For each element sigma of the absolute Galois group Gal((K) over bar /K), let (K) over bar(sigma) be the fixed field in (K) over bar of sigma. We show that the torsion subgroup of A((K) over bar(sigma)) is infinite for all sigma is an element of Gal((K) over bar /K) outside of some set of Haar measure zero. This proves the number field case of a conjecture of W.-D. Geyer and M. Jarden.
展开▼
机译：设A为在数字字段K上定义的非零阿贝尔变种，设bar上的（K）为K的固定代数闭包。对于绝对Galois群Gal（（K）上bar / K）的每个元素sigma，令bar（sigma）上的（K）为sigma bar上（K）的固定字段。我们证明，对于所有sigma，A（（K）over bar（sigma）的扭力子组都是无限的，它是在一组Haar测度零之外的Gal（（K）over bar / K）的元素。这证明了W.-D猜想的数域情况。盖尔（Geyer）和贾登（M. Jarden）。
展开▼
