Ramified covers of abelian varieties over torsion fields

2022/06/03 by Lior Bary‐Soroker, Arno Fehm, Bary-Soroker, Lior +3 · 3 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2206.01582

Abstract

We study rational points on ramified covers of abelian varieties over certain infinite Galois extensions of ℚ. In particular, we prove that every elliptic curve E over ℚ has the weak Hilbert property of Corvaja-Zannier both over the maximal abelian extension ℚ^{\rm ab} of ℚ, and over the field ℚ(A_{\rm tor}) obtained by adjoining to ℚ all torsion points of some abelian variety A over ℚ.

Cited by

• Hilbert properties of varieties
• Fibration theorems for varieties with the weak Hilbert property
• Hilbert irreducibility for abelian varieties over function fields of characteristic zero

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• Torsion dans un produit de courbes elliptiques
• The rational points on certain Abelian varieties over function fields
• Torsion points of abelian varieties with values in infinite extensions over a p-adic field
• An analogue of a conjecture of Rasmussen and Tamagawa for abelian varieties over function fields