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Answer by Joël for Topology in Arithmetic
Dear user02138, you may be interested in the Bombieri-Lang conjecture. It has a weak form and a strong form. The latter is:If $X$ s a smooth variety over a number field $K$ which is of general type...
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Conjectured by Mordell and later proved by Faltings, a non-singular algebraic curve of genus $g$ over $\mathbb{Q}$ has finitely many rational points if $g > 1$. Since the genus of the Fermat curve...
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