PAC fields over number fields

Moshe Jarden[1]

  • [1] Tel Aviv University School of Mathematics Ramat Aviv, Tel Aviv 69978, Israel

Journal de Théorie des Nombres de Bordeaux (2006)

  • Volume: 18, Issue: 2, page 371-377
  • ISSN: 1246-7405

Abstract

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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 .

How to cite

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Jarden, Moshe. "PAC fields over number fields." Journal de Théorie des Nombres de Bordeaux 18.2 (2006): 371-377. <http://eudml.org/doc/249647>.

@article{Jarden2006,
abstract = {We prove that if $K$ is a number field and $N$ is a Galois extension of $\mathbb\{Q\}$ which is not algebraically closed, then $N$ is not PAC over $K$.},
affiliation = {Tel Aviv University School of Mathematics Ramat Aviv, Tel Aviv 69978, Israel},
author = {Jarden, Moshe},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {field arithmetic; PAC fields},
language = {eng},
number = {2},
pages = {371-377},
publisher = {Université Bordeaux 1},
title = {PAC fields over number fields},
url = {http://eudml.org/doc/249647},
volume = {18},
year = {2006},
}

TY - JOUR
AU - Jarden, Moshe
TI - PAC fields over number fields
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2006
PB - Université Bordeaux 1
VL - 18
IS - 2
SP - 371
EP - 377
AB - We prove that if $K$ is a number field and $N$ is a Galois extension of $\mathbb{Q}$ which is not algebraically closed, then $N$ is not PAC over $K$.
LA - eng
KW - field arithmetic; PAC fields
UR - http://eudml.org/doc/249647
ER -

References

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  1. M. D. Fried, M. Jarden, Field Arithmetic. Second edition, revised and enlarged by Moshe Jarden, Ergebnisse der Mathematik (3) 11, Springer, Heidelberg, 2005. Zbl1055.12003MR2102046
  2. W.-D. Geyer, M. Jarden, PSC Galois extensions of Hilbertian fields. Mathematische Nachrichten 236 (2002), 119–160. Zbl1007.12003MR1888560
  3. G. J. Janusz, Algebraic Number Fields. Academic Press, New York, 1973. Zbl0307.12001MR366864
  4. M. Jarden, A. Razon, Pseudo algebraically closed fields over rings. Israel Journal of Mathematics 86 (1994), 25–59. Zbl0802.12007MR1276130
  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. Zbl0924.11092MR1355075
  6. S. Lang, Introduction to Algebraic Geometry. Interscience Publishers, New York, 1958. Zbl0095.15301MR100591
  7. J. Neukirch, Kennzeichnung der p -adischen und der endlichen algebraischen Zahlkörper. Inventiones mathematicae 6 (1969), 296–314. Zbl0192.40102MR244211
  8. A. Razon, Splitting of ℚ ˜ / ℚ . Archiv der Mathematik 74 (2000), 263–265 Zbl0954.12001MR1742636

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