You need the field extension to have transcendence degree 1 over $\mathbb{C}$ to get a Riemann surface. More generally, you can get an algebraic curve at least for every transcendence degree 1 extension over an algebraically closed field. Chapter I of Hartshorne does this in detail, I don't know an analytic approach.
|
1 | [made Community Wiki] | ||
|
|
||||
