• Corpus ID: 202583501

Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields

@article{Shankar2019ExceptionalJO,
  title={Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields},
  author={Ananth N. Shankar and Arul Shankar and Yunqing Tang and Salim Tayou},
  journal={arXiv: Number Theory},
  year={2019}
}
Given a K3 surface $X$ over a number field $K$, we prove that the set of primes of $K$ where the geometric Picard rank jumps is infinite, assuming that $X$ has everywhere potentially good reduction. The result is a special case of a more general one on exceptional classes for K3 type motives associated to GSpin Shimura varieties and several other applications are given. As a corollary, we give a new proof of the fact that $X_{\overline{K}}$ has infinitely many rational curves. 
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