PAC fields over number fields

Jarden, Moshe

doi:10.5802/jtnb.550

Jarden, Moshe ¹

¹ Tel Aviv University School of Mathematics Ramat Aviv, Tel Aviv 69978, Israel

Journal de théorie des nombres de Bordeaux, Tome 18 (2006) no. 2, pp. 371-377.

Résumé
Abstract

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

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

MR Zbl

DOI : 10.5802/jtnb.550

Affiliations des auteurs :

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, Tome 18 (2006) no. 2, pp. 371-377. doi : 10.5802/jtnb.550. https://www.numdam.org/articles/10.5802/jtnb.550/

Bibliographie
Cité par

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Bary-Soroker, Lior On pseudo algebraically closed extensions of fields, Journal of Algebra, Volume 322 (2009) no. 6, p. 2082 | DOI:10.1016/j.jalgebra.2009.07.003
Haran, Dan; Jarden, Moshe; Pop, Florian The Absolute Galois Group of the Field of Totally S-Adic Numbers, Nagoya Mathematical Journal, Volume 194 (2009), p. 91 | DOI:10.1017/s0027763000009648
Bary-Soroker, Lior; Jarden, Moshe PAC fields over finitely generated fields, Mathematische Zeitschrift, Volume 260 (2008) no. 2, p. 329 | DOI:10.1007/s00209-007-0276-3

Cité par 3 documents. Sources : Crossref