Stable extensions and fields with the global density property

Michael Fried, Moshe Jarden
1976 Canadian Journal of Mathematics - Journal Canadien de Mathematiques  
Introduction. For a field M we denote by M s and M respectively the separable closure and the algebraic closure of M. If F is a variety which is defined over M, then we denote by V(M) the set of all if-rational points of V. M is said to be pseudo-algebraically closed (PAC) field, if V(M) ^ 0 for every non-void abstract variety V defined over M. It can be shown that then V(M) is dense in V(M) in the Zariski M -topology. Suppose now that M is equipped with an absolute value w. M is said to have
more » ... M is said to have the density property with respect to w, if V(M) is w-dense in V(M W ) for every abstract variety V defined over M. Here M w is the completion of M with respect to w.
doi:10.4153/cjm-1976-074-6 fatcat:rdqj6ekdnvbmtghbqbfob3rnui