The Hilbert property for arithmetic schemes
Volume 206 / 2022
Acta Arithmetica 206 (2022), 115-126
MSC: Primary 14G99; Secondary 14G05, 14G40.
DOI: 10.4064/aa211214-16-11
Published online: 8 December 2022
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.
