Pseudo algebraically closed fields over rings |
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Authors: | Moshe Jarden Aharon Razon |
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Institution: | (1) School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel |
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Abstract: | We prove that for almost allσ ∈G ℚ the field
has the following property: For each absolutely irreducible affine varietyV of dimensionr and each dominating separable rational mapϕ:V→
there exists a point a ∈
such thatϕ(a) ∈ ℤr. We then say that
is PAC over ℤ. This is a stronger property then being PAC. Indeed we show that beside the fields
other fields which are algebraic over ℤ and are known in the literature to be PAC are not PAC over ℤ. |
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Keywords: | |
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