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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.

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Misunderstanding of Hodge conjecture

The Hodge conjecture implies that the functor $R\colon M_{num}(k,\mathbb{Q})→HS(\mathbb{Q})$ is fully faithful when $k$ is the algebraic closure of $\mathbb{Q}$, not $\mathbb{Q}$ itself, as your exam …
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