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SUMMARY:Fei Hu (Harvard)
DTSTART:20220427T140000Z
DTEND:20220427T153000Z
DTSTAMP:20260422T220542Z
UID:STAGE/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/56/">U
 niformity for rational points</a>\nby Fei Hu (Harvard) as part of STAGE\n\
 nLecture held in Room 2-449 in the MIT Simons Building.\n\nAbstract\nWe di
 scuss the proof of Proposition 8.1 in [DGH]\, which gives a uniform bound 
 for the intersection of rational points $C(\\overline\\mathbb{Q})$ of a cu
 rve $C$ of large modular height in an abelian variety $A$ and a finite ran
 k subgroup $\\Gamma\\subseteq A(\\overline\\mathbb{Q})$.\nThe number of la
 rge points can be handled by a standard application of the Vojta and\nMumf
 ord inequalities.\nThe key of [DGH] is to bound the number of those small 
 points using the so-called New Gap Principle.\n\nWe then deduce the unifor
 m boundedness of rational/torsion points of curves in [DGH]\, i.e.\, their
  Theorems 1.1\, 1.2\, and 1.4\, from the above Proposition 8.1 (for curves
  of large modular height) and some other classical results (taking care of
  curves of small modular height).\n
LOCATION:https://researchseminars.org/talk/STAGE/56/
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