PAC fields over number fields
Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 2, pp. 371-377.

We prove that if K is a number field and N is a Galois extension of which is not algebraically closed, then N is not PAC over K.

Soient K un corps de nombres et N une extension galoisienne de qui n’est pas algébriquement close. Alors N n’est pas PAC sur K.

DOI: 10.5802/jtnb.550
Jarden, Moshe 1

1 Tel Aviv University School of Mathematics Ramat Aviv, Tel Aviv 69978, Israel
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Jarden, Moshe. PAC fields over number fields. Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 2, pp. 371-377. doi : 10.5802/jtnb.550. http://www.numdam.org/articles/10.5802/jtnb.550/

[1] M. D. Fried, M. Jarden, Field Arithmetic. Second edition, revised and enlarged by Moshe Jarden, Ergebnisse der Mathematik (3) 11, Springer, Heidelberg, 2005. | MR | Zbl

[2] W.-D. Geyer, M. Jarden, PSC Galois extensions of Hilbertian fields. Mathematische Nachrichten 236 (2002), 119–160. | MR | Zbl

[3] G. J. Janusz, Algebraic Number Fields. Academic Press, New York, 1973. | MR | Zbl

[4] M. Jarden, A. Razon, Pseudo algebraically closed fields over rings. Israel Journal of Mathematics 86 (1994), 25–59. | MR | Zbl

[5] M. Jarden, A. Razon, Rumely’s local global principle for algebraic P𝒮C fields over rings. Transactions of AMS 350 (1998), 55–85. | MR | Zbl

[6] S. Lang, Introduction to Algebraic Geometry. Interscience Publishers, New York, 1958. | MR | Zbl

[7] J. Neukirch, Kennzeichnung der p-adischen und der endlichen algebraischen Zahlkörper. Inventiones mathematicae 6 (1969), 296–314. | MR | Zbl

[8] A. Razon, Splitting of ˜/. Archiv der Mathematik 74 (2000), 263–265 | MR | Zbl

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