On the Picard number of K3 surfaces over number fields

François Charles (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Domaines: Géométrie algébrique [math.AG]

François Charles. On the Picard number of K3 surfaces over number fields. Algebra & Number Theory, 2014, 8 (1), pp.1-17. ⟨10.2140/ant.2014.8.1⟩. ⟨hal-00843098⟩