Galois cohomology of elliptic curves over anticyclotomic extensions

Abstract

Let $K$ be an imaginary quadratic field and $p$ be an odd prime number. Let $E/\mathbb{Q}$ be an elliptic curve with good ordinary reduction at $p$. We study the Iwasawa theory of $E$ over the anticyclotomic ${\mathbb{Z}}_p$-extension of $K$ by adopting a unifying framework. We also study the Galois cohomology of the dual Selmer group of $E$ over the unique ${\mathbb{Z}}_p^2$-extension of $K$ as well as over the anticyclotomic extension of $K$.