Riemann Surface

The Riemann surface $S$ of the Algebraic Function Field $K$ is the set of nontrivial discrete valuations on $K$. Here, the set $S$ corresponds to the Ideals of the Ring $A$ of Integers of $K$ over $\Bbb{C}(z)$. ($A$ consists of the elements of $K$ that are Roots of Monic Polynomials over $\Bbb{C}[z]$.)

See also Algebraic Function Field, Ideal, Ring

References

Fischer, G. (Ed.). Plates 123-126 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, pp. 120-123, 1986.