Publikationsdetails

On a Galois property of fields generated by the torsion of an abelian variety

verfasst von
Sara Checcoli, Gabriel A. Dill
Abstract

In this article, we study a certain Galois property of subextensions of $k(A_{\mathrm{tors}})$, the minimal field of definition of all torsion points of an abelian variety $A$ defined over a number field $k$. Concretely, we show that each subfield of $k(A_{\mathrm{tors}})$ which is Galois over $k$ (of possibly infinite degree) and whose Galois group has finite exponent is contained in an abelian extension of some finite extension of $k$. As an immediate corollary of this result and a theorem of Bombieri and Zannier, we deduce that each such field has the Northcott property, i.e. does not contain any infinite set of algebraic numbers of bounded height.

Organisationseinheit(en)
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Externe Organisation(en)
Université Grenoble Alpes (UGA)
Rheinische Friedrich-Wilhelms-Universität Bonn
Typ
Artikel
Journal
Bulletin of the London Mathematical Society
Band
56
Seiten
3530-3541
ISSN
0024-6093
Publikationsdatum
03.11.2024
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
Elektronische Version(en)
https://doi.org/10.1112/blms.13149 (Zugang: Geschlossen)
https://doi.org/10.48550/arXiv.2306.12138 (Zugang: Offen)