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SUMMARY:Xinyu Fang (Harvard)
DTSTART:20250403T210000Z
DTEND:20250403T223000Z
DTSTAMP:20260422T220514Z
UID:STAGE/128
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/128/">
 Outline of the argument for Mordell's conjecture</a>\nby Xinyu Fang (Harva
 rd) as part of STAGE\n\nLecture held in Room 2-449 in the MIT Simons Build
 ing.\n\nAbstract\nI will present an outline of the argument for the proof 
 of Mordell's conjecture\, following Section 5 of Lawrence-Venkatesh. Speci
 fically\, I will give an overview of two key inputs: the existence of a go
 od abelian-by-finite family (the Kodaira-Parshin family) and the finitenes
 s of rational points whose fiber along the finite map has large Galois orb
 its (proven using p-adic Hodge theory). Then\, I will explain how to reduc
 e Mordell's conjecture to these key inputs.\n\nReference:\n\n$\\bullet$ <a
  href="https://link.springer.com/article/10.1007/s00222-020-00966-7">Lawre
 nce and Venkatesh\, Diophantine problems and $p$-adic period mappings</a>\
 , Section 5.\n
LOCATION:https://researchseminars.org/talk/STAGE/128/
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