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GEOMETRIC REPRESENTATION IN THE THEORY OF PSEUDO-FINITE FIELDS

Published online by Cambridge University Press:  02 May 2017

ÖZLEM BEYARSLAN  and
ZOÉ CHATZIDAKIS
ÖZLEM BEYARSLAN
Affiliation:
BOĞAZIÇI UNIVERSITY FACULTY OF ARTS AND SCIENCE DEPARTMENT OF MATHEMATICS 34342, BEBEK-ISTANBUL, TURKEYE-mail:[email protected]
ZOÉ CHATZIDAKIS
Affiliation:
CNRS (UMR 8553) - ECOLE NORMALE SUPÉRIEURE 45 RUE D’ULM 75230 PARIS CEDEX 05, FRANCEE-mail:[email protected]
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Abstract

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group which is geometrically represented in a pseudo-finite field must be abelian.

Keywords

03C6003C6512F1012L12pseudo-finite fields
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 3 , September 2017 , pp. 1132 - 1139
Copyright
Copyright © The Association for Symbolic Logic 2017 

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References

REFERENCES

Beyarslan, Ö. and Hrushovski, E., On algebraic closure in pseudo-finite fields, this Journal, vol. 77 (2012), pp. 1057–1066.Google Scholar
Chatzidakis, Z., Some properties of the absolute Galois group of a Hilbertian field . Israel Journal of Mathematics, vol. 55 (1986), no. 2, pp. 173–183.CrossRefGoogle Scholar
Engler, A. J. and Prestel, A., Valued Fields , Springer Monographs in Mathematics, vol. 11, Springer-Verlag, Berlin, 2005.Google Scholar
Fried, M. and Jarden, M., Field Arithmetic , Ergebnisse der Mathematik und ihrer Grenzgebiet, vol. 11, Springer-Verlag, Berlin, 2005.Google Scholar
Hrushovski, E., Pseudo-finite fields and related structures , Model Theory and Applications (Bélair, L., Chatzidakis, Z., D’Aquino, P., Marker, D., Otero, M., Point, F., and Wilkie, A., editors), Quaderni di Matematica, vol. 11, Aracne, Rome, 2005, pp. 151–212.Google Scholar
Koenigsmann, J., Products of Absolute Galois Groups . International Mathematics Research Notices, vol. 24 (2005), no. 24, pp. 1465–1486.Google Scholar