Time：10:00, Friday, November 24, 2023
Venue：E4-233 & ZOOM
ZOOM ID：959 8466 2147
PASSCODE：587750
Speaker：Sinnou David, Sorbonne Université
Biography：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.
Title：On Lehmer problem on semi-abelian varieties
Abstract：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.
