On the Mordell-Weil Ranks of supersingular abelian varieties over ${\mathbb{Z}}_p^2$-extensions

Cédric Dion, Jishnu Ray

Let $p$ be a fixed odd prime and let $K$ be an imaginary quadratic field in which $p$ splits. Let $A$ be an abelian variety defined over $K$ with supersingular reduction at both pr…