English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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

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