Algebraic Function Field

A finite extension $K=\Bbb{Z}(z)(w)$ of the Field $\Bbb{C}(z)$ of Rational Functions in the indeterminate $z$, i.e., $w$ is a Root of a Polynomial $a_0+a_1\alpha+a_2\alpha^2+\ldots +a_n\alpha^n$, where $a_i\in\Bbb{C}(z)$.

See also Algebraic Number Field, Riemann Surface