Abstract
Abstract
We show that a nontrivial abelian variety over a Hilbertian field in which the weak Mordell–Weil theorem holds admits infinitely many torsors with period any given
n>1
that is not divisible by the characteristic. The corresponding statement with “period” replaced by “index” is plausible but open, and it seems much more challenging. We show that for every infinite, finitely generated field K, there is an elliptic curve
E_{/K}
which admits infinitely many torsors with index any given
n>1
.
Subject
Applied Mathematics,General Mathematics
Reference70 articles.
1. Lectures on the conjecture of Birch and Swinnerton-Dyer;Arithmetic of L-functions,2011
2. On the Mordell–Weil lattices;Comment. Math. Univ. St. Pauli,1990
3. Exponents of elliptic curves;Dokl. Akad. Nauk SSSR (N.S.),1957
4. Period and index of genus one curves over global fields;Math. Ann.,2012
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献