Ramified covers of abelian varieties over torsion fields

Lior Bary-Soroker; Arno Fehm; Sebastian Petersen

doi:10.1515/crelle-2023-0077

Ramified covers of abelian varieties over torsion fields

Lior Bary-Soroker, Arno Fehm, Sebastian Petersen

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

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 and Zannier both over the maximal abelian extension ℚab of ℚ, and over the field ℚ (A tor) obtained by adjoining to ℚ all torsion points of some abelian variety A over ℚ.

Original language	English
Pages (from-to)	185-211
Number of pages	27
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2023
Issue number	805
DOIs	https://doi.org/10.1515/crelle-2023-0077
State	Published - 1 Dec 2023

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1515/crelle-2023-0077

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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 and Zannier both over the maximal abelian extension ℚab of ℚ, and over the field ℚ (A tor) obtained by adjoining to ℚ all torsion points of some abelian variety A over ℚ.",

author = "Lior Bary-Soroker and Arno Fehm and Sebastian Petersen",

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AU - Fehm, Arno

AU - Petersen, Sebastian

PY - 2023/12/1

Y1 - 2023/12/1

N2 - 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 and Zannier both over the maximal abelian extension ℚab of ℚ, and over the field ℚ (A tor) obtained by adjoining to ℚ all torsion points of some abelian variety A over ℚ.

AB - 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 and Zannier both over the maximal abelian extension ℚab of ℚ, and over the field ℚ (A tor) obtained by adjoining to ℚ all torsion points of some abelian variety A over ℚ.

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U2 - 10.1515/crelle-2023-0077

DO - 10.1515/crelle-2023-0077

M3 - مقالة

SN - 0075-4102

VL - 2023

SP - 185

EP - 211

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 805

ER -

Ramified covers of abelian varieties over torsion fields

Abstract

All Science Journal Classification (ASJC) codes

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