Moduli of abelian varieties and p-divisible groups : Density of Hecke orbits, and a conjecture by Grothendieck

Abstract

Conference on Arithmetic Geometry, Gottingen 17 July - 11 August 2006. In the week 7 – 11 August 2006 we give a course, and here are notes for that course. Our main topic will be: geometry and arithmetic of Ag ⊗Fp, the moduli space of polarized abelian varieties in positive characteristic. We illustrate properties of these topics, and available techniques by treating two topics: Density of ordinary Hecke orbits and A conjecture by Grothendieck on deformations of p-divisible groups.