The Hilbert property for arithmetic schemes
arXiv:2212.01138
Abstract
We extend the usual Hilbert property for varieties over fields to arithmetic schemes over integral domains by demanding the set of near-integral points (as defined by Vojta) to be non-thin. We then generalize results of Bary-Soroker-Fehm-Petersen and Corvaja-Zannier by proving several structure results related to products and finite étale covers of arithmetic schemes with the Hilbert property.
10 pages, accepted for publication in Acta Arithmetica