On the Picard number of K3 surfaces over number fields

Charles, François

doi:10.2140/ant.2014.8.1

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On the Picard number of K3 surfaces over number fields

François Charles

Vol. 8 (2014), No. 1, 1–17

DOI: 10.2140/ant.2014.8.1

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 compute explicitly the Picard number of any given K3 surface over a number field.

Keywords

K3 surfaces, Picard number, Néron–Severi group

Mathematical Subject Classification 2010

Primary: 14J28

Secondary: 14C22, 14G25, 11G35

Milestones

Received: 1 February 2012

Revised: 20 September 2012

Accepted: 4 November 2012

Published: 20 April 2014

Authors

François Charles
Institut de Recherche Mathématiques de Rennes Université de Rennes 1 Campus de Beaulieu 35042 Rennes France
http://perso.univ-rennes1.fr/francois.charles/

Vol. 8, No. 1, 2014