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学术科研

Algebra & Combinatorics Seminar

Application of (mixed) Ax-Schanuel to counting rational points on curves

演讲者：高紫阳（法国国家科学研究中心，巴黎 Jussieu 数学研究所）
时间：2018-11-12 09:00-10:00
地点：慧园3栋 415报告厅

报告摘要

With Philipp Habegger we recently proved a height inequality, using which (and previous work of Remond 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, partly joint with Vesselin Dimitrov and Philipp Habegger.