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

Research output: Working paper/Preprint › Preprint

Authors

  • Sara Checcoli
  • Gabriel A. Dill

Research Organisations

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Details

Original languageFrench
Publication statusE-pub ahead of print - 31 Jul 2023

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.

Keywords

    math.NT, 11J95, 11R32

Cite this

On a Galois property of fields generated by the torsion of an abelian variety. / Checcoli, Sara; Dill, Gabriel A.
2023.

Research output: Working paper/Preprint › Preprint

Checcoli, S., & Dill, G. A. (2023). On a Galois property of fields generated by the torsion of an abelian variety. Advance online publication.
Checcoli S, Dill GA. On a Galois property of fields generated by the torsion of an abelian variety. 2023 Jul 31. Epub 2023 Jul 31.
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