Random Galois extensions of Hilbertian fields
Lior Bary-Soroker1; Arno Fehm2
1 School of Mathematical Sciences Tel Aviv University Ramat Aviv Tel Aviv 69978 Israel
2 Universität Konstanz Fachbereich Mathematik und Statistik Fach D 203 78457 Konstanz Germany
Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 1, pp. 31-42.

Let L be a Galois extension of a countable Hilbertian field K. Although L need not be Hilbertian, we prove that an abundance of large Galois subextensions of L/K are.

Soit L une extension galoisienne d’un corps K hilbertien et dénombrable. Bien que L ne soit pas nécessairement hilbertien, nous montrons qu’il existe beaucoup de grandes sous-extensions de L/K qui le sont.

DOI: 10.5802/jtnb.823
Lior Bary-Soroker 1; Arno Fehm 2

1 School of Mathematical Sciences Tel Aviv University Ramat Aviv Tel Aviv 69978 Israel
2 Universität Konstanz Fachbereich Mathematik und Statistik Fach D 203 78457 Konstanz Germany 
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Lior Bary-Soroker; Arno Fehm. Random Galois extensions of Hilbertian fields. Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 1, pp. 31-42. doi : 10.5802/jtnb.823. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.823/

[1] Lior Bary-Soroker, On the characterization of Hilbertian fields. International Mathematics Research Notices, 2008. | MR | Zbl

[2] Lior Bary-Soroker, On pseudo algebraically closed extensions of fields. Journal of Algebra 322(6) (2009), 2082–2105. | MR | Zbl

[3] Lior Bary-Soroker and Arno Fehm, On fields of totally S-adic numbers. http://arxiv.org/abs/1202.6200, 2012.

[4] M. Fried and M. Jarden, Field Arithmetic. Ergebnisse der Mathematik III 11. Springer, 2008. 3rd edition, revised by M. Jarden. | MR | Zbl

[5] Dan Haran, Hilbertian fields under separable algebraic extensions. Invent. Math. 137(1) (1999), 113–126. | MR | Zbl

[6] Dan Haran, Moshe Jarden, and Florian Pop, The absolute Galois group of subfields of the field of totally S-adic numbers. Functiones et Approximatio, Commentarii Mathematici, 2012. | MR

[7] Moshe Jarden, Large normal extension of Hilbertian fields. Mathematische Zeitschrift 224 (1997), 555–565. | MR | Zbl

[8] Thomas J. Jech, Set Theory. Springer, 2002. | MR | Zbl

[9] Serge Lang, Diophantine Geometry. Interscience Publishers, 1962. | MR | Zbl

[10] Jean-Pierre Serre, Topics in Galois Theory. Jones and Bartlett Publishers, 1992. | MR | Zbl

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