Ruled Function Fields

Let $L = {L_1}({x_1}) = {L_2}({x_2}) \supset K$ where ${x_i}$ is transcendental over ${L_i}$, and ${L_i}$ is a finitely generated transcendence degree 1 extension of $K$, $i = 1,2$. If the genus of ${L_1}/K = 0$, then ${L_1}$ and ${L_2}$ are $K$-isomorphic. If the genus of ${L_1}/K > 0$, then ${L_1}... View More