Abstract
Let G be a commutative algebraic group over a finitely generated infinite field K of characteristic p. We prove that every extension of K contained in the field obtained by adjoining to K all prime-to-p torsion points of G is Hilbertian. We also determine when the field obtained by adjoining to K all torsion points of G has this property. This extends results of Moshe Jarden on abelian varieties.
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Fehm, A., Petersen, S. Hilbertianity of division fields of commutative algebraic groups. Isr. J. Math. 195, 123–134 (2013). https://doi.org/10.1007/s11856-012-0064-6
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DOI: https://doi.org/10.1007/s11856-012-0064-6