On the distribution of the Picard ranks of the reductions of a K3 surface

We report on our results concerning the distribution of the geometric Picard ranks of K 3 surfaces under reduction modulo various primes. In the situation that rk Pic S K ¯ is even, we introduce a quadratic character, called the jump character, such that rk Pic S F ¯ p > rk Pic S K ¯ for all good...

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Veröffentlicht in:	Research in number theory 2020-09, Vol.6 (3), Article 27
Hauptverfasser:	Costa, Edgar, Elsenhans, Andreas-Stephan, Jahnel, Jörg
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics Number Theory
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