Specializations and a local homeomorphism theorem for real Riemann surfaces of rings

M. J. de la Puente

Vol. 176 (1996), No. 2, 427–442

DOI: 10.2140/pjm.1996.176.427

Abstract

Let ϕ : k → A and f : A → R be ring morphisms, R a real ring. We prove that if f : A → R is étale, then the corresponding mapping between real Riemann surfaces S_r(f) : S_r(R∕k) → S_r(A∕k) is a local homeomorphism. Several preparatory results are proved, as well. The most relevant among these are: (1) a Chevalley’s theorem for real Riemann surfaces on the preservation of constructibility via S_r(f), and (2) an analysis of the closure operator on real Riemann surfaces. Constructible sets are dealt with by means of a suitable first-order language.

Mathematical Subject Classification 2000

Primary: 14P10

Secondary: 12D15

Milestones

Received: 3 January 1992

Revised: 19 December 1995

Published: 1 December 1996