On the distribution of the Picard ranks of the reductions of a K3 surface
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We report on our results concerning the distribution of the geometric Picard ranks of K3 surfaces under reduction modulo various primes. In the situation that rk Pic S [subscript overline K] is even, we introduce a quadratic character, called the jump character, such that rk Pic S [subscript overline F][subscript > Pic S [subscript overline K] for all good primes at which the character evaluates to (-1).
Date issued
2020-06Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Research in Number Theory
Publisher
Springer Science and Business Media LLC
Citation
Costa, Edgar et al. "On the distribution of the Picard ranks of the reductions of a K3 surface." Research in Number Theory 6, 3 (June 2020): 27 © 2020 The Author(s)
Version: Final published version
ISSN
2522-0160
2363-9555