11 février 2020

Yunqing Tang (IMO)
Picard ranks of reductions of K3 surfaces over global fields

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Lieu : salle 3L15 bâtiment 307

Résumé : For a K3 surface X over a number field with potentially good reduction everywhere,
we prove that there are infinitely many primes modulo which the reduction of X has larger
geometric Picard rank than that of the generic fiber X. A similar statement still holds true for
ordinary K3 surfaces over global function fields. In this talk, I will present the proofs via the
intersection theory on GSpin Shimura varieties and also discuss various applications. These
results are generalizations of the work of Charles on exceptional isogenies between reductions
of a pair of elliptic curves. This talk is based on joint work with Ananth Shankar, Arul Shankar,
and Salim Tayou and with Davesh Maulik and Ananth Shankar.

Picard ranks of reductions of K3 surfaces over global fields  Version PDF