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Mar 14, 2019 at 22:49 comment added Vesselin Dimitrov Still the original form of the question, with the finitely generated group instead of the generalization to finite rank groups (allowing for $C / \mathbb{C}$), is almost trivially equivalent to the original Mordell $\#C(K) < \infty$ conjecture for $C/K$ over number fields.
Mar 14, 2019 at 22:11 history answered François Brunault CC BY-SA 4.0