Diophantine Problems and \(p\)-adic Period Mappings (after Lawrence and Venkatesh) (Fall 2021)

The goal of this seminar is to go over the recent proof of Faltings's theorem by Lawrence and Venkatesh [LV]. The method of this proof, which heavily involves \(p\)-adic Hodge theory rather than heights and abelian varieties, may also be applied to higher dimensional varieties. We will follow the program outlined here.

Schedule

Sept 24
Caleb Ji
Faltings's theorem: comparison of approaches
I will give an overview of both Faltings's original proof of the Mordell conjecture and the Chabauty-Kim approach. Then I will outline the strategy of the proof given by Lawrence and Venkatesh.
Oct 1
Caleb Ji
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