On the Picard number of K3 surfaces over number fields

Abstract

We discuss some aspects of the behavior of specialization at a finite place of Néron-Severi groups of K3 surfaces over number fields. We give optimal lower bounds for the Picard number of such specializations, thus answering a question of Elsenhans and Jahnel. As a consequence of these results, we show that it is possible to explicitly compute the Picard number of any given K3 surface over a number field.

14 pages, comments welcome

References in corpus (1)

• Vector bundles on a K3 surface

Cited by in corpus (2)

• Construction de courbes sur les surfaces K3 [d'après Bogomolov-Hassett-Tschinkel, Charles, Li-Liedtke, Madapusi Pera, Maulik...]
• Variation of Neron-Severi ranks of reductions of K3 surfaces