Israel Journal of Mathematics

, Volume 86, Issue 1–3, pp 25–59 | Cite as

Pseudo algebraically closed fields over rings

  • Moshe Jarden
  • Aharon Razon


We prove that for almost allσG ℚ the field\(\tilde{\mathbb{Q}}\) has the following property: For each absolutely irreducible affine varietyV of dimensionr and each dominating separable rational mapϕ:V\(\tilde{\mathbb{Q}}\) there exists a point a ∈\(\mathbb{A}\) such thatϕ(a) ∈ ℤr. We then say that\(\tilde{\mathbb{Q}}\) is PAC over ℤ. This is a stronger property then being PAC. Indeed we show that beside the fields\(\tilde{\mathbb{Q}}\) other fields which are algebraic over ℤ and are known in the literature to be PAC are not PAC over ℤ.


Finite Group Branch Point Galois Extension Irreducible Polynomial Finite Extension 
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Copyright information

© The Magnes Press 1994

Authors and Affiliations

  1. 1.School of Mathematical SciencesRaymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv UniversityTel AvivIsrael

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