Wan-Lin Li

Rank stability of elliptic curves over prime cyclic extensions of function fields

Let $\ell$ be an odd prime number. Let $E$ be a non-isotrivial elliptic curve defined over the global function field $K = \mathbb{F}_q(t)$ such that $(q, 6) = 1$ and $q \equiv 1 \mod \ell$. We show that as $q$ grows arbitrarily large, both analytic and algebraic ranks of $E$ do not grow upon base change to $100\%$ of $...