Number Theory Seminar

Title: Bruno Winckler (Université de Bordeaux)

Speaker: Lehmer's problem and arithmetic intersection.

Abstract: I will talk about a work in progress regarding lower bounds for the canonical height of algebraic points on elliptic curves with complex multiplications, aiming for the conjecture of Lehmer. I try to prove a better and more explicit version of a weaker form of this inequality, due to Laurent, by using Arakelov's intersection theory: a theorem of Faltings and Hriljac links the canonical height on a elliptic curve and an intersection number on its regular minimal model.
This computation needs some explicit bounds of sums indexed by well-chosen prime numbers, obtained thanks to an explicit version of Cebotarev theorem. I will give such a version.