Algebraic and Arithmetic Geometry Seminar

# Algebraic classes in mixed characteristic and André's p-adic periods

## by Giuseppe Ancona (Université de Strasbourg)

Europe/Rome
Aula Magna (Department of Mathematics)

### Aula Magna

#### Department of Mathematics

Description

(Joint work with D. Fratila) Motivated by the study of algebraic classes in mixed characteristic, we define a countable subalgebra of ${\Bbb Q}_p$ which we call the algebra of “Andre's p-adic periods”. We will explain the analogy and the difference between these p-adic periods and the classical complex periods. For instance, they both contain several examples of special values of classical functions (logarithm, gamma function, …) and they share transcendence properties. On the other hand, the classical Tannakian formalism which is used to bound the transcendence degree of complex periods has to be modified in order to be used in the p-adic setting. We will discuss concrete examples of all these instances though elliptic curves and Kummer extensions.