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K3 surfaces: rational points and Picard numbers

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K3 surfaces: rational points and Picard numbers

It is a widely accepted philosophy that the arithmetic of a variety,say over a number field, is governed by its geometry. Indeed, weexpect many rational points, if any, on Del Pezzo surfaces, while onsurfaces of general type, we expect that the rational points are notdense. On K3 surfaces, as for Del Pezzo surfaces, we expect morerational points for higher Picard numbers: for high enough Picardnumber, rational points are potentially dense by a result of Tschinkeland Bogomolov. In this talk, I will highlight some results on thearithmetic of K3 surfaces. I will focus on diagonal quartic surfaces,surfaces with two elliptic fibrations, and on computing Picardnumbers.

- Variétés rationnelles

Détails :

Orateur / Oratrice : Ronald van Luijk
Date : 13 mai 2011
Horaire : 14h30 - 15h30
Lieu : Salle W