Number theory days

Session

Géométrie arithmétique et théorie de Galois

26 juin 2014, 09:00

Salle de réunions (Université Lille 1)

Présidents de session

Géométrie arithmétique et théorie de Galois

• Niels Borne
• Pierre Debes

18. Points rationnels et zéro-cycles dans les fibrations

Olivier Wittenberg (École normale supérieure)

26/06/2014 09:00

Géométrie arithmétique et théorie de Galois

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...

19. Oort groups and lifting problems

David Harbater (University of Pennsylvania)

26/06/2014 10:30

Géométrie arithmétique et théorie de Galois

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...

1. The arithmetic of tori over various fields

David Harari (Université Paris-Sud)

26/06/2014 11:45

Géométrie arithmétique et théorie de Galois

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.

0. Generalised perfectoid rings and perfectoid spaces

Lorenzo Ramero (Université Lille 1)

26/06/2014 15:30

Géométrie arithmétique et théorie de Galois

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.

23. Recent Progress in Bogomolov's Program: A Survey

Aaron Silberstein (University of Pennsylvania)

26/06/2014 17:00

Géométrie arithmétique et théorie de Galois

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...