On the Picard number of K3 surfaces over number fields

Details On the Picard number of K3 surfaces over number fields On the Picard number of K3 surfaces over number fields

2011-11-17

arxiv.org/abs/1111.4117v1

Mathematics

Algebraic Geometry

14 pages, comments welcome

Scientific paper

We discuss some aspects of the behavior of specialization at a finite place of N\'eron-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.

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