Ranks of elliptic curves over Z_p^2-extensions

Abstract

Let $E$ be an elliptic curve with good reduction at a fixed odd prime $p$ and $K$ an imaginary quadratic field where $p$ splits. We give a growth estimate for the Mordell-Weil rank of $E$ over finite extensions inside the ${\mathbb{Z}}_p^2$-extension of $K$.

15 pages, plus references