# Number theory days

23-27 June 2014
Université Lille 1
Europe/Paris timezone

## Recent Progress in Bogomolov's Program: A Survey

26 Jun 2014, 17:00
1h
Salle de réunions (Université Lille 1)

### Salle de réunions

#### Université Lille 1

U.M.R. CNRS 8524 U.F.R. de Mathématiques 59 655 Villeneuve d'Ascq Cédex
Arithmetic geometry and Galois theory

### Speaker

Aaron Silberstein (University of Pennsylvania)

### Description

Given a field $K$, finitely generated and of transcendence degree $2$ over the algebraic closure of a prime field, we may now reconstruct $K$ from the maximal $2$-step nilpotent pro-$\ell$ quotient of its absolute Galois group. This allows us to construct a complete (albeit countably infinite) set of geometric obstructions for an element of the Grothendieck-Teichmüller group to come from an element of the absolute Galois group of $\mathbb{Q}$.

### Presentation Materials

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