Number of Rational Points on Curves
发布时间：2019年04月12日
浏览次数：6627
发布者: He Liu
主讲人： Ziyang Gao (Paris 7 & CNRS)
活动时间： 从 2019-04-18 11:00 到 12:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室
With Philipp Habegger we recently proved a height inequality, using which (and previous work of Rémond in the realm of the classical Bombieri-Faltings-Vojta method) one can prove that the number of rational points on a 1-parameter family of curves of genus g is bounded in terms of g, degree of the field, the family and the Mordell-Weil rank of each individual curve in this family. In this talk I’ll explain how the height inequality yields this bound, and then explain how this method can be generalized to an arbitrary family via mixed Ax-Schanuel for universal abelian varieties. This is work in progress, joint with Vesselin Dimitrov and Philipp Habegger.
