4 papers
math.AG2024
A mixed fibration theorem for Hilbert irreducibility on non-proper varieties
Cedric Luger
We prove that the weak Hilbert property ascends along a morphism of varieties over an arbitrary field of characteristic zero, under suitable assumptions.
math.AG2024
Hilbert irreducibility for integral points on punctured linear algebraic groups
Cedric Luger
Let be a number field, let be a smooth integral variety over , and assume that there exists a finite set of finite places of such that the -integral points on…
math.AG2024
Products of varieties with many integral points
Cedric Luger
Corvaja and Zannier asked whether a smooth projective integral variety with a dense set of rational points over a number field satisfies the weak Hilbert property. We introduce an…
math.AG2022
The Hilbert property for arithmetic schemes
Cedric Luger
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…