On the Picard number of K3 surfaces over number fields

By Franccois Charles. 2011

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We discuss some aspects of the behavior of specialization at a finite place of Neron-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.

Subfields: Algebra and Number Theory, Artificial Intelligence, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d6f210a22fa956bed51a9dfef9dc54e8b86ac1e6

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