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)