On the Picard number of K3 surfaces over number fields

2011/11/17 by François Charles, Charles, François
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · doi:10.48550/arxiv.1111.4117

openalex publication_date 2011/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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