Abstract. Every nontrivial abelian variety over a Hilbertian field in which the weak Mordell-Weil theorem holds admits infinitely many torsors with period any n > 1 which is not divisible by the characteristic. The corresponding statement with "period" replaced by "index" is plausible but 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 n > 1.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.