On local uniformization of orderings.

Abstract

“Let A be the coordinate ring of the real plane, i.e., A = R[X, Y ], where X, Y are algebraically independent over the field of real numbers R. The purpose of this paper is to describe all the valuation rings of A which are compatible with some prime cone of A, i.e., to give a description of all the points of the real Riemann surface Sr(A/R). Furthermore, we explain the geometric meaning of these points and indicate the specialization relations among them.”