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 Tate-Shafarevich group of $E$ or not. Thank you in advance.

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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 Tate-Shafarevich group of $E$ or not. Thank you in advance. |
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cohomology group, and with non-trivial coefficients too. So I am not at all optimistic. – Kevin Buzzard Apr 28 '11 at 19:46