Residues in Algebraic Function Fields of One Variable

Abstract

Let L/K be an algebraic function field with Trdeg(L/K) = 1. The set X of all discrete valuation rings R with K ⊂ R and Q(R) = L is called the “non-singular model” of L/K, or the “abstract Riemann surface” of L/K. It is well-known that X together with L is also the set of local rings of a non-singular projective algebraic curve defined over K.