16:00
Mordell-Weil groups as Galois modules
Abstract
Let $E/k$ be an elliptic curve over a number field and $K/k$ a Galois extension with group $G$. What can we say about $E(K)$ as a Galois module? Not just what complex representations appear, but its structure as a $\mathbb{Z}[G]$-module. We will look at some examples with small $G$.