| Résume | In the recent breakthrough on the uniform Mordell-Lang problem by Dimitrov-Gao-Habegger and Kühne, their key new theorem is a uniform Bogomolov conjecture for curves over number fields. In this talk, we introduce a refinement and generalization of the uniform Bogomolov conjecture over global fields, as a consequence of bigness of some adelic line bundles. The treatment is based on the new theory of adelic line bundles of Yuan--Zhang and the admissible pairing over curves of Zhang. |
