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

@article{JTNB_2006__18_2_371_0,
     author = {Jarden, Moshe},
     title = {PAC fields over number fields},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {371--377},
     publisher = {Universit\'e Bordeaux 1},
     volume = {18},
     number = {2},
     year = {2006},
     doi = {10.5802/jtnb.550},
     zbl = {05135402},
     mrnumber = {2289430},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jtnb.550/}
}

TY  - JOUR
AU  - Jarden, Moshe
TI  - PAC fields over number fields
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2006
SP  - 371
EP  - 377
VL  - 18
IS  - 2
PB  - Université Bordeaux 1
UR  - http://www.numdam.org/articles/10.5802/jtnb.550/
DO  - 10.5802/jtnb.550
LA  - en
ID  - JTNB_2006__18_2_371_0
ER  -

%0 Journal Article
%A Jarden, Moshe
%T PAC fields over number fields
%J Journal de théorie des nombres de Bordeaux
%D 2006
%P 371-377
%V 18
%N 2
%I Université Bordeaux 1
%U http://www.numdam.org/articles/10.5802/jtnb.550/
%R 10.5802/jtnb.550
%G en
%F JTNB_2006__18_2_371_0

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. http://www.numdam.org/articles/10.5802/jtnb.550/

Bibliographie
Cité par

[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 P $𝒮$ C 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 $\tilde{ℚ} / ℚ$ . Archiv der Mathematik 74 (2000), 263–265 | MR | Zbl

Cité par Sources :