On pseudo-nullity of fine Mordell-Weil group

Abstract

Let $E$ be an elliptic curve defined over $\mathbb{Q}$ with good ordinary reduction at a prime $p\ge 5$, and let $F$ be an imaginary quadratic field. Under appropriate assumptions, we show that the Pontryagin dual of the fine Mordell-Weil group of $E$ over the ${\mathbb{Z}}_p^2$-extension of $F$ is pseudo-null as a module over the Iwasawa algebra of the group ${\mathbb{Z}}_p^2$.

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