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arXiv · 1111.4117

On the Picard number of K3 surfaces over number fields

François Charles
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Abstract

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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François Charles. 2011-11-17. On the Picard number of K3 surfaces over number fields. https://arxiv.org/abs/1111.4117

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