Random Galois extensions of Hilbertian fields

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

Journal de Théorie des Nombres de Bordeaux (2013)

  • Volume: 25, Issue: 1, page 31-42
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Bary-Soroker, Lior, and Fehm, Arno. "Random Galois extensions of Hilbertian fields." Journal de Théorie des Nombres de Bordeaux 25.1 (2013): 31-42. <http://eudml.org/doc/275812>.

@article{Bary2013,
abstract = {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.},
affiliation = {School of Mathematical Sciences Tel Aviv University Ramat Aviv Tel Aviv 69978 Israel; Universität Konstanz Fachbereich Mathematik und Statistik Fach D 203 78457 Konstanz Germany},
author = {Bary-Soroker, Lior, Fehm, Arno},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
month = {4},
number = {1},
pages = {31-42},
publisher = {Société Arithmétique de Bordeaux},
title = {Random Galois extensions of Hilbertian fields},
url = {http://eudml.org/doc/275812},
volume = {25},
year = {2013},
}

TY - JOUR
AU - Bary-Soroker, Lior
AU - Fehm, Arno
TI - Random Galois extensions of Hilbertian fields
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2013/4//
PB - Société Arithmétique de Bordeaux
VL - 25
IS - 1
SP - 31
EP - 42
AB - 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.
LA - eng
UR - http://eudml.org/doc/275812
ER -

References

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  1. Lior Bary-Soroker, On the characterization of Hilbertian fields. International Mathematics Research Notices, 2008. Zbl1217.12003MR2439555
  2. Lior Bary-Soroker, On pseudo algebraically closed extensions of fields. Journal of Algebra 322(6) (2009), 2082–2105. Zbl1213.12006MR2542832
  3. Lior Bary-Soroker and Arno Fehm, On fields of totally S -adic numbers. http://arxiv.org/abs/1202.6200, 2012. Zbl06424158
  4. M. Fried and M. Jarden, Field Arithmetic. Ergebnisse der Mathematik III 11. Springer, 2008. 3rd edition, revised by M. Jarden. Zbl1145.12001MR2445111
  5. Dan Haran, Hilbertian fields under separable algebraic extensions. Invent. Math. 137(1) (1999), 113–126. Zbl0933.12003MR1702139
  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. Zbl1318.12001MR2931667
  7. Moshe Jarden, Large normal extension of Hilbertian fields. Mathematische Zeitschrift 224 (1997), 555–565. Zbl0873.12001MR1452049
  8. Thomas J. Jech, Set Theory. Springer, 2002. Zbl1007.03002MR1940513
  9. Serge Lang, Diophantine Geometry. Interscience Publishers, 1962. Zbl0115.38701MR142550
  10. Jean-Pierre Serre, Topics in Galois Theory. Jones and Bartlett Publishers, 1992. Zbl0746.12001MR1162313

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