algebraic function field

A finite extension K = Q(z)(w) of the field Q(z) of rational functions in the indeterminate z, i.e., w is a root of a polynomial a_0 + a_1 α + a_2 α^2 + ... + a_n α^n, where a_i element Q(z). Function fields are sometimes called algebraic function fields.

local field | number field | Riemann surface