Around the Manin-Mumford Conjecture and l-adic Representations
Speaker(s): Aurelien Galateau (Universit´e de Franche-Comt´)
Time: April 18 - April 26, 2019
Venue: Room 29, Quan Zhai, BICMR
Date: April 18 Time: 14:00-16:00 Venue: Room 29, Quan Zhai, BICMR
Date: April 23, April 26 Time: 14:00-16:00 Venue: Room 77201, Jingchunyuan 78, BICMR
The Manin-Mumford conjecture describes the distribution of torsion points on subvarieties of abelian varieties. It was proven by Raynaud, and more precise versions were given later by Coleman, Buium and others. I will describe these classical works and explain how some fine properties of the l-adic representations associated to the torsion of abelian varieties can be used to give uniform bounds in the Manin-Mumford problem. I will finally discuss effective results on the distribution of special points on powers of modular curves.