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SUMMARY:Philipp Habegger (University of Basel)
DTSTART:20210401T120000Z
DTEND:20210401T130000Z
DTSTAMP:20260423T005754Z
UID:AGNTISTA/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGNTISTA/35/
 ">Uniformity for the Number of Rational Points on a Curve</a>\nby Philipp 
 Habegger (University of Basel) as part of Algebraic Geometry and Number Th
 eory seminar - ISTA\n\n\nAbstract\nBy 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 proof. Many authors\, including Bombier
 i\, de Diego\, Parshin\, Rémond\, Vojta\, proved upper bounds for the num
 ber of K-rational points. I will discuss joint work with Vesselin Dimitrov
  and Ziyang Gao where we prove that the number of points on the curve is b
 ounded from above as a function of K\, the genus\, and the rank of the Mor
 dell-Weil group of the curve's Jacobian. We follow Vojta's approach to the
  Mordell Conjecture. I will explain the new feature: an inequality for the
  Néron-Tate height in a family of abelian varieties. It allows us to boun
 d from above the number of points whose height is in the intermediate rang
 e.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/35/
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