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GEOMETRIC REPRESENTATION IN THE THEORY OF PSEUDO-FINITE FIELDS

  • ÖZLEM BEYARSLAN (a1) and ZOÉ CHATZIDAKIS (a2)
Abstract
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.

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[1] BeyarslanÖ. and HrushovskiE., On algebraic closure in pseudo-finite fields, this Journal, vol. 77 (2012), pp. 10571066.
[2] ChatzidakisZ., Some properties of the absolute Galois group of a Hilbertian field . Israel Journal of Mathematics, vol. 55 (1986), no. 2, pp. 173183.
[3] EnglerA. J. and PrestelA., Valued Fields , Springer Monographs in Mathematics, vol. 11, Springer-Verlag, Berlin, 2005.
[4] FriedM. and JardenM., Field Arithmetic , Ergebnisse der Mathematik und ihrer Grenzgebiet, vol. 11, Springer-Verlag, Berlin, 2005.
[5] HrushovskiE., Pseudo-finite fields and related structures , Model Theory and Applications (BélairL., ChatzidakisZ., D’AquinoP., MarkerD., OteroM., PointF., and WilkieA., editors), Quaderni di Matematica, vol. 11, Aracne, Rome, 2005, pp. 151212.
[6] KoenigsmannJ., Products of Absolute Galois Groups . International Mathematics Research Notices, vol. 24 (2005), no. 24, pp. 14651486.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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