Hilbertian fields and Galois representations
-
Lior Bary-Soroker
,
Arno Fehm
Abstract
We prove a new Hilbertianity criterion for fields in towers whose steps are Galois with Galois group either abelian or a product of finite simple groups. We then apply this criterion to fields arising from Galois representations. In particular we settle a conjecture of Jarden on abelian varieties.
Funding source: Lion Foundation Konstanz
Funding source: von Humboldt Foundation
Funding source: German-Israeli Foundation for Scientific Research and Development
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: Priority Program 1489
This work was greatly influenced by the papers [J. Inst. Math. Jussieu 9 (2010), no. 3, 477–480] of Jarden and [J. Inst. Math. Jussieu 12 (2013), no. 2, 237–247] of Thornhill. The authors would like to thank Sebastian Petersen for interesting discussions on this subject and Dror Speiser for pointing out the application in Section 5.1. We are also grateful to the referee for her/his helpful suggestions.
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Refined semiclassical asymptotics for fractional powers of the Laplace operator
- Projective metric number theory
- Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
- Right simple singularities in positive characteristic
- Discriminants and Artin conductors
- Hilbertian fields and Galois representations
- Simple endotrivial modules for quasi-simple groups
- A reconstruction theorem for abelian categories of twisted sheaves
- Hyperkähler manifolds of Jacobian type
- The algebra of essential relations on a finite set
Articles in the same Issue
- Frontmatter
- Refined semiclassical asymptotics for fractional powers of the Laplace operator
- Projective metric number theory
- Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
- Right simple singularities in positive characteristic
- Discriminants and Artin conductors
- Hilbertian fields and Galois representations
- Simple endotrivial modules for quasi-simple groups
- A reconstruction theorem for abelian categories of twisted sheaves
- Hyperkähler manifolds of Jacobian type
- The algebra of essential relations on a finite set
