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# Number theory days

23-27 juin 2014
Université Lille 1
Europe/Paris timezone
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# Contribution

Université Lille 1 - Salle de réunions
Arithmetic geometry and Galois theory

# Recent Progress in Bogomolov's Program: A Survey

## Intervenant(s)

• Aaron SILBERSTEIN

## 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 $\mathbb{Q}$.