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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
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Questions about analogy between Spec Z and 3-manifolds
My post is not an answer, but rather a suggestion of work which belongs to this circle of ideas : Sugiyama gives a geometric analog of the Birch and Swinnerton-Dyer conjecture in http://geoquant.mi.ra …