Variation of Néron-Severi Ranks of Reductions of K3 Surfaces

Abstract

We study the behavior of geometric Picard ranks of K3 surfaces over Q under reduction modulo primes. We compute these ranks for reductions of smooth quartic surfaces modulo all primes p < 2 in several representative examples and investigate the resulting statistics. 
DOI: 10.1080/10586458.2014.947054

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