A uniform Bogomolov type of theorem for curves over global fields

A uniform Bogomolov type of theorem for curves over global fields

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Xinyi Yuan, BICMR

Online Talk 

*Please note the change in day/ time*

Zoom link:  https://princeton.zoom.us/j/97126136441

Passcode: The three digit integer that is the cube of the sum of its digits

In the recent breakthrough on the uniform Mordell-Lang problem by Dimitrov-Gao-Habegger and Kuhne, their key result is a uniform Bogomolov type of theorem 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 in the setting of Arakelov geometry. The treatment is based on the new theory of adelic line bundles of Yuan-Zhang and the admissible pairing over curves of Zhang.