Présidents de session
Arithmetic geometry and Galois theory
- Niels Borne
- Pierre Debes
Olivier Wittenberg
(École normale supérieure)
26/06/2014 09:00
Arithmetic geometry and Galois theory
Si X est une variété projective et lisse définie sur un corps de nombres, la ``méthode des fibrations'' pour étudier l'ensemble des points rationnels de X ou le groupe de Chow des zéro-cycles de X vise à ramener les questions que l'on pose pour X (par exemple: existence d'un point ou d'un zéro-cycle de degré 1) aux mêmes questions pour les fibres d'un morphisme dominant f:X->P^1. Le but de...
David Harbater
(University of Pennsylvania)
26/06/2014 10:30
Arithmetic geometry and Galois theory
The Oort conjecture states that every cyclic branched cover of curves in characteristic p can be lifted to such a cover in characteristic zero. This raises the more general question of which finite groups G have the property that every G-Galois branched cover of curves in characteristic p can be lifted to characteristic zero. While this can be viewed as analogous to the inverse Galois...
David Harari
(Université Paris-Sud)
26/06/2014 11:45
Let T be an algebraic torus defined over a number field K. In the case of a number field, obstructions to local-global principles for T are well understood thanks to work by Voskresenskii and Sansuc. We consider the case K=k(t) for different fields k (quasi-finite, p-adic) and extend the classical results in this context.
Lorenzo Ramero
(Université Lille 1)
26/06/2014 15:30
Arithmetic geometry and Galois theory
Scholze's theory of perfectoid rings and perfectoid spaces is rather recent, but it has already had some spectacular applications to étale cohomology, p-adic Hosge theory and p-adic representations. I will present a generalization of this theory that I am developing in collaboration with Ofer Gabber. I will also explain the questions that have led us to this generalization.
Aaron Silberstein
(University of Pennsylvania)
26/06/2014 17:00
Arithmetic geometry and Galois theory
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...
