All Questions

Let $L/K$ be a finite Galois extensions of number fields and $E/K$ be an elliptic curve. Denote by $\mathcal{F}$ the localization map \begin{equation} \mathcal{F}: H^1(G,E(L)) \rightarrow \bigoplus_{v ...

I am trying to understand an argument of Corollary 7.3 from Silverman's The Arithmetic of Elliptic Curves. I am stuck and I would appreciate any explanations. Let $E$ be an elliptic curve over $K$, ...

Let $E$ be an elliptic curve over $\mathbb{Q}_p$ with potential good reduction. I was told that if $F$ is the smallest Galois extension over $\mathbb{Q}_p$ such that $E$ has good reduction then the ...

Neron-Ogg-Shafarevich criterion states that an elliptic curve $E$ over a local field $K$ has a good reduction if and only if the Tate module $T_{\ell}(E)$ is unramified for some prime $\ell$ which ...

Is there a simple description of the group Q_p*/(Q_p*)^2 where Q_p denotes the p-adic integers? I am doing descent calculations for elliptic curves, and so am most interested in the case p = 2. ...