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Aug 12, 2014 at 0:46 vote accept user56793
Aug 10, 2014 at 22:34 comment added S. Carnahan Your claim "$V_\ell(A) \cong V_\ell(B)$ if and only if $A \sim B$" doesn't hold if you take the isomorphism in the category of vector spaces over $\mathbb{Q}_\ell$. If you want an analogue of Galois-module isomorphisms determining isogeny type, you should consider adding structure to your topological $V_\ell$, like a class of periods.
Aug 10, 2014 at 22:12 answer added Will Sawin timeline score: 2
Aug 10, 2014 at 19:02 answer added abx timeline score: 1
Aug 10, 2014 at 18:36 history asked user56793 CC BY-SA 3.0