The Hilbert property for arithmetic schemes

2022/12/02 by Cedric Luger, Luger, Cedric · 2 citations
Computer Science · Mathematics · #14G40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary: 14G99. Secondary: 14G05

paper · pdf · doi:10.48550/arxiv.2212.01138

openalex publication_date 2022/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Hilbert properties of varieties
• Fibration theorems for varieties with the weak Hilbert property

Related

• Products of varieties with many integral points
• Elliptic Fibrations and Hilbert Property
• On the Hilbert Property and the Fundamental Group of Algebraic Varieties
• Hilbert properties of varieties
• Integral points on Hilbert moduli schemes