Christian Wuthrich

The Mordell-Weil group as a Galois module

Let E be an elliptic curve over a number field k and let K/k be a finite Galois extension with group G, typically cyclic or dihedral. What can we say about the Modell-Weil group E(K) as a Z[G]-module?
Let p be an odd prime dividing the degree [K : k]. I wish to present results on how to determine the p-adic completion of E(K) as a Zp[G]-module using, if possible, only local information and information of E over k. I will also address the case when k is a p-adic field.