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Pré-Publication, Document De Travail Année : 2023

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

Sara Checcoli

Résumé

In this article, we study a certain Galois property of subextensions of k(A_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_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.
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Dates et versions

hal-04148573 , version 1 (03-07-2023)

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  • HAL Id : hal-04148573 , version 1

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Sara Checcoli, Gabriel A. Dill. On a Galois property of fields generated by the torsion of an abelian variety. 2023. ⟨hal-04148573⟩
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