Upcoming Talks

Ist logo

Uniformity for the Number of Rational Points on a Curve

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

Date: Thursday, April 1, 2021 14:00 - 15:00
Speaker: Philipp Habegger (University of Basel)
Location: https://mathseminars.org/seminar/AGNTISTA
Series: Mathematics and CS Seminar
Host: Tim Browning

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 proof. Many authors, including Bombieri, de Diego, Parshin, Rémond, Vojta, proved upper bounds for the number 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 bounded from above as a function of K, the genus, and the rank of the Mordell-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 bound from above the number of points whose height is in the intermediate range.


Qr image
Download ICS Download invitation
Back to eventlist