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DTSTART:20210328T030000
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DTSTAMP:20260406T042324Z
UID:1617278400@ist.ac.at
DTSTART:20210401T140000
DTEND:20210401T150000
DESCRIPTION:Speaker: Philipp Habegger\nhosted by Tim Browning\nAbstract: By
  Faltings's Theorem\, formerly known as the Mordell Conjecture\, a smooth 
 projective curve of genus at least 2 that is defined over a number field K
  has at most finitely many K-rational points. Votja later gave a second pr
 oof. Many authors\, including Bombieri\, de Diego\, Parshin\, Rémond\, Vo
 jta\, proved upper bounds for the number of K-rational points. I will disc
 uss joint work with Vesselin Dimitrov and Ziyang Gao where we prove that t
 he number of points on the curve is bounded from above as a function of K\
 , the genus\, and the rank of the Mordell-Weil group of the curve's Jacobi
 an. We follow Vojta's approach to the Mordell Conjecture. I will explain t
 he new feature: an inequality for the Néron-Tate height in a family of ab
 elian varieties. It allows us to bound from above the number of points who
 se height is in the intermediate range.
LOCATION:https://mathseminars.org/seminar/AGNTISTA\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Philipp Habegger: Uniformity for the Number of Rational Points on a
  Curve
URL:https://talks-calendar.ista.ac.at/events/3096
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