Rings of continuous functions and the branch set of a covering

Abstract

This paper gives a characterization of the branch set of a finite covering X → S X\to S of a topological space S S , by means of finite C ( S ) C(S) -subalgebras A A of C ( X ) C(X) that separate points in X X and the module Ω A / C ( S ) \Omega _{A/C(S)} of its Kähler differentials.