Abelian varieties over cyclic fields

Abstract

Let $K$ be a field of characteristic $\neq 2$ such that every finite separable extension of $K$ is cyclic. Let $A$ be an abelian variety over $K$. If $K$ is infinite, then $A(K)$ is Zariski-dense in $A$. If $K$ is not locally finite, the rank of $A$ over $K$ is infinite.

Locations

• American Journal of Mathematics - View
• arXiv (Cornell University) - PDF