ABELIAN VARIETIES OVER LARGE ALGEBRAIC FIELDS WITH INFINITE TORSION

作者：Zywina David^*

来源：Israel Journal of Mathematics, 2016, 211(1): 493-508.

DOI：10.1007/s11856-015-1268-3

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.

• 出版日期2016-2