Periods and heights of special moduli

Abstract: A classical problem in algebraic geometry is to understand moduli which are "special" in the sense that the varieties they correspond to have additional algebraic structure not present at a general fibre. A method of André approaches this problem by studying the transcendence properties of certain period functions computed at the special moduli, and this allows one to bound the heights of these moduli. Unfortunately, however, the method is restricted by the lack of a suitable p-adic interpretation of the period functions.

We give an overview of this method. If time permits, we will describe work in progress to give a p-adic interpretation of these periods, removing the restriction.

algebraic geometrynumber theory

Audience: researchers in the topic

Séminaire de géométrie arithmétique et motivique (Paris Nord)