Pseudo algebraically closed fields over rings

Moshe Jarden*, Aharon Razon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We prove that for almost all σ ∈G ℚ the field {Mathematical expression} has the following property: For each absolutely irreducible affine variety V of dimension r and each dominating separable rational map φ{symbol}:V→ {Mathematical expression} there exists a point a ∈ {Mathematical expression} such that φ{symbol}(a) ∈ ℤr. We then say that {Mathematical expression} is PAC over ℤ. This is a stronger property then being PAC. Indeed we show that beside the fields {Mathematical expression} other fields which are algebraic over ℤ and are known in the literature to be PAC are not PAC over ℤ.

Original languageEnglish
Pages (from-to)25-59
Number of pages35
JournalIsrael Journal of Mathematics
Issue number1-3
StatePublished - Oct 1994


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