Thời gian: 16h30, thứ Năm, 12/09/2024

Tóm tắt: Mordell's conjecture states that for a smooth projective curve of genus at least 2 over a number field K, it has only finitely many K-rational points. Faltings (1983) gave a well-known proof by Arakelov methods. This talk is an overview of the proof of Lawrence and Venkatesh (2020), in which they introduce a new method to prove the nondensity of integral points by a beautiful combination between $p$-adic Hodge theory, the functional transcendence of $p$-adic period mappings, and big monodromy results.

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