Hello,
I would like to know whether, given an elliptic curve $E$ over $\mathbb{Q}$, there is a "natural" topological space associated to $E$ whose fundamental group is (isomorphic to) the TateShafarevich group of $E$ or not. Thank you in advance.
Hello, I would like to know whether, given an elliptic curve $E$ over $\mathbb{Q}$, there is a "natural" topological space associated to $E$ whose fundamental group is (isomorphic to) the TateShafarevich group of $E$ or not. Thank you in advance. 

