On the distribution of the Picard ranks of the reductions of a K3 surface
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40993_2020_Article_204.pdf
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Author(s)
Costa, Edgar
Elsenhans, Andreas-Stephan
Jahnel, Jörg
Martins Dias Costa, Edgar Jose
Date Issued
June 2020
Journal
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
Abstract
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).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
http://dx.doi.org/10.1007/s40993-020-00204-2
