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
Format: Artikel
Sprache:eng
Schlagworte:
Number theory
Subgroups
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Beschreibung
Zusammenfassung: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.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2021.0043