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Variétés rationnelles

Horaires : Le vendredi 13 mai 2011, 14h30-15h30

Lieu : salle W

K3 surfaces: rational points and Picard numbers

Ronald van Luijk (Leiden - page personnelle)

It is a widely accepted philosophy that the arithmetic of a variety, say over a number field, is governed by its geometry. Indeed, we expect many rational points, if any, on Del Pezzo surfaces, while on surfaces of general type, we expect that the rational points are not dense. On K3 surfaces, as for Del Pezzo surfaces, we expect more rational points for higher Picard numbers: for high enough Picard number, rational points are potentially dense by a result of Tschinkel and Bogomolov. In this talk, I will highlight some results on the arithmetic of K3 surfaces. I will focus on diagonal quartic surfaces, surfaces with two elliptic fibrations, and on computing Picard numbers.


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