6th Distinguished Lecture丨On Lehmer problem on semi-abelian varieties

2023-11-22 15:22:18


地点:E4-233 & ZOOM

ZOOM会议号959 8466 2147


主讲人:Sinnou David, Sorbonne Université

主讲人简介:Sinnou David is currently a professor at Sorbonne Université. For his doctoral studies, he joined the University Pierre et Marie Curie, Paris (UPMC), worked under the supervision of Prof. Daniel Bertrand, and defended his Ph.D. in 1989. He has been the Deputy Director of Institut de Mathématiques de Jussieu-Paris Rive Gauche and then deputy scientific director of INSMI CNRS, in charge of international affairs. He is specialized in diophantine geometry.

报告题目:On Lehmer problem on semi-abelian varieties

报告摘要:The classical Lehmer problem states that the Weil height of a (non torsion) algebraic number of degree $d$ over the rational numbers is at least $c/d$ where $c$ is universal. While still open, good partial results are known. This conjecture is also known to generalize to general multiplicative groups (for these questions it is enough to consider a power of $G_m$ as well as to abelian varieties, provided one replaces the Weil height by the Néron-Tate height. However, while a semi-abelian variety over a number field can also be endowed with a normalized height, natural generalisations of Lehmer's question fail to hold due to a natural obstruction reminiscent of unlikely intersections appearing in Pink-Zilber conjectures. We propose a generalisation of Lehmer's conjecture taking it into account and prove partial results for semi-abelian varieties having a CM (small dimension) base.