## Details

Originalsprache | Französisch |
---|---|

Publikationsstatus | Elektronisch veröffentlicht (E-Pub) - 31 Juli 2023 |

## Abstract

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

2023.

Publikation: Arbeitspapier/Preprint › Preprint

*On a Galois property of fields generated by the torsion of an abelian variety*. Vorabveröffentlichung online.

}

TY - UNPB

T1 - On a Galois property of fields generated by the torsion of an abelian variety

AU - Checcoli, Sara

AU - Dill, Gabriel A.

N1 - 16 pages, added Section 4 on the validity of the main result over other ground fields, comments are welcome

PY - 2023/7/31

Y1 - 2023/7/31

N2 - 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.

AB - 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.

KW - math.NT

KW - 11J95, 11R32

M3 - Preprint

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

ER -