Kuykian fields

Arno Fehm; Moshe Jarden; Sebastian Petersen

doi:10.1515/FORM.2011.094

Kuykian fields

Arno Fehm^*, Moshe Jarden, Sebastian Petersen

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The Kuykian conjecture for a Hilbertian field K says that if A/K is an abelian variety, then every intermediate field of K(A _tor)/K is Hilbertian. We prove the Kuykian conjecture in the following cases: (a) K is finitely generated (over its prime field). (b) K D F _s [σ] for almost all ε 2 Gal(K) ^e, where F is a finitely generated field. (c) K D F _ins, where F is the quotient field of a complete local domain of dimension at least 2.

Original language	English
Pages (from-to)	1013-1022
Number of pages	10
Journal	Forum Mathematicum
Volume	24
Issue number	5
DOIs	https://doi.org/10.1515/FORM.2011.094
State	Published - Sep 2012

Keywords

Abelian varieties
Hilbertian fields
Torsion points

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10.1515/FORM.2011.094

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abstract = "The Kuykian conjecture for a Hilbertian field K says that if A/K is an abelian variety, then every intermediate field of K(A tor)/K is Hilbertian. We prove the Kuykian conjecture in the following cases: (a) K is finitely generated (over its prime field). (b) K D F s [σ] for almost all ε 2 Gal(K) e, where F is a finitely generated field. (c) K D F ins, where F is the quotient field of a complete local domain of dimension at least 2.",

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AB - The Kuykian conjecture for a Hilbertian field K says that if A/K is an abelian variety, then every intermediate field of K(A tor)/K is Hilbertian. We prove the Kuykian conjecture in the following cases: (a) K is finitely generated (over its prime field). (b) K D F s [σ] for almost all ε 2 Gal(K) e, where F is a finitely generated field. (c) K D F ins, where F is the quotient field of a complete local domain of dimension at least 2.

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Kuykian fields

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Keywords

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