On uniformity conjectures for abelian varieties and K3 surfaces

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  • Authors:
  • Martin Orr
  • Alexei N. Skorobogatov
  • Yuri G. Zarhin


We discuss logical links among uniformity conjectures concerning K3 surfaces and abelian varieties of bounded dimension defined over number fields of bounded degree. The conjectures concern the endomorphism algebra of an abelian variety, the Néron-Severi lattice of a K3 surface, and the Galois invariant subgroup of the geometric Brauer group.

Bibliographical metadata

Original languageEnglish
Pages (from-to)1665-1702
Number of pages38
JournalAmerican Journal of Mathematics
Issue number6
Publication statusPublished - 4 Dec 2021