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On uniformity conjectures for abelian varieties and K3 surfaces
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 143, Number 6, December 2021
- pp. 1665-1702
- 10.1353/ajm.2021.0043
- Article
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Abstract
abstract:
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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