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Random Galois extensions of Hilbertian fields. (English. French summary) Zbl 1387.12002
Summary: 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.

MSC:
12E25 Hilbertian fields; Hilbert’s irreducibility theorem
12F10 Separable extensions, Galois theory
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References:
[1] Lior Bary-Soroker, On the characterization of Hilbertian fields. International Mathematics Research Notices, 2008. · Zbl 1217.12003
[2] Lior Bary-Soroker, On pseudo algebraically closed extensions of fields. Journal of Algebra 322(6) (2009), 2082-2105. · Zbl 1213.12006
[3] Lior Bary-Soroker and Arno Fehm, On fields of totally \(S\)-adic numbers. http://arxiv.org/abs/1202.6200, 2012. · Zbl 1392.11090
[4] M. Fried and M. Jarden, Field Arithmetic. Ergebnisse der Mathematik III 11. Springer, 2008. 3rd edition, revised by M. Jarden. · Zbl 1145.12001
[5] Dan Haran, Hilbertian fields under separable algebraic extensions. Invent. Math. 137(1) (1999), 113-126. · Zbl 0933.12003
[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. · Zbl 1318.12001
[7] Moshe Jarden, Large normal extension of Hilbertian fields. Mathematische Zeitschrift 224 (1997), 555-565. · Zbl 0873.12001
[8] Thomas J. Jech, Set Theory. Springer, 2002. · Zbl 1007.03002
[9] Serge Lang, Diophantine Geometry. Interscience Publishers, 1962. · Zbl 0115.38701
[10] Jean-Pierre Serre, Topics in Galois Theory. Jones and Bartlett Publishers, 1992. · Zbl 0746.12001
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