@article{4a6e0c3570914934acd213b89dfe9028,
title = "On uniformity conjectures for abelian varieties and K3 surfaces",
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{\'e}ron-Severi lattice of a K3 surface, and the Galois invariant subgroup of the geometric Brauer group.",
author = "Martin Orr and Skorobogatov, {Alexei N.} and Zarhin, {Yuri G.}",
note = "Funding Information: Manuscript received November 9, 2018. Research of the first and second authors supported by the EPSRC grant EP/M020266/1; research of the third author supported in part by Simons Foundation Collaboration grant #585711. American Journal of Mathematics 143 (2021), 1665–1702. {\textcopyright} 2021 by Johns Hopkins University Press. Publisher Copyright: {\textcopyright} 2021 by Johns Hopkins University Press.",
year = "2021",
month = dec,
day = "4",
doi = "10.1353/ajm.2021.0043",
language = "English",
volume = "143",
pages = "1665--1702",
journal = "American Journal of Mathematics",
issn = "0002-9327",
publisher = "Johns Hopkins University Press",
number = "6",
}