We prove new results on the distribution of rational points on ramified covers of abelian
varieties over finitely generated fields. Our results do not seem to be in the range of other …

We prove that the integral points are potentially Zariski dense in the complement of a
reduced effective singular anticanonical divisor in a smooth del Pezzo surface, with the …

We study the preservation of the Hilbert property and of the weak Hilbert property under
base change in field extensions. In particular we show that these properties are preserved if …

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 …

Let be a connected linear algebraic group over a number field, let be a finitely generated
Zariski dense subgroup of, and let be a thin set, in the sense of Serre. We prove that, if is …

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 …

Let $ f (t_1,\ldots, t_r, X)\in\mathbb {Z}[t_1,\ldots, t_r, X] $ be irreducible and let $ a_1,\ldots,
a_r\in\mathbb {Z}\smallsetminus\{0,\pm 1\} $. Under a necessary ramification assumption on …

For an abelian variety $ A/K $ we study finite generation properties of the profinite group
$\Gal (K_\tors (A)/K) $ and of certain closed normal subgroups thereof, where $ K_\tors (A) …

One of the guiding principles in Diophantine geometry is that, if an algebraic variety
contains" many" integral points, then there is a geometric reason explaining their …

Hilbert properties of varieties Page 1 Hilbert properties of varieties Arno Fehm1 AHGT Seminar
February 2024 1Technische Universität Dresden Arno Fehm Hilbert properties of varieties …