On uniformity conjectures for abelian varieties and K3 surfaces

On uniformity conjectures for abelian varieties and K3 surfaces

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 N\'eron-Severi lattice of a K3 surface, and the Galoi...

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Veröffentlicht in:American journal of mathematics 2021-12, Vol.143 (6), p.1665-1702
Hauptverfasser: Orr, Martin, Skorobogatov, Alexei N, Zarhin, Yuri G
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Number theory
Subgroups
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container_title American journal of mathematics
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creator Orr, Martin
Skorobogatov, Alexei N
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description 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 N\'eron-Severi lattice of a K3 surface, and the Galois invariant subgroup of the geometric Brauer group.
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Subgroups
title On uniformity conjectures for abelian varieties and K3 surfaces
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