On uniformity conjectures for abelian varieties and K3 surfaces

Orr, Martin; Skorobogatov, Alexei N.; Zarhin, Yuri G.

doi:10.1353/ajm.2021.0043

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Journal Article

On uniformity conjectures for abelian varieties and K3 surfaces

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Skorobogatov, Alexei N.
Max Planck Institute for Mathematics, Max Planck Society;

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Zarhin, Yuri G.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1353/ajm.2021.0043
(Publisher version)

https://doi.org/10.48550/arXiv.1809.01440
(Preprint)

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MPIM Preprint series 2018-52.pdf
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Citation

Orr, M., Skorobogatov, A. N., & Zarhin, Y. G. (2021). On uniformity conjectures for abelian varieties and K3 surfaces. American Journal of Mathematics, 143(6), 1665-1702. doi:10.1353/ajm.2021.0043.

Cite as: https://hdl.handle.net/21.11116/0000-0009-B378-6

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 Neron-Severi lattice of a K3 surface, and the Galois invariant
subgroup of the geometric Brauer group.