Drinfeld Ring

Let be a smooth geometrically connected projective curve over with a prime power. Let be a fixed closed point of but not necessarily -rational. A Drinfeld ring is the ring , i.e., the sections of the sheaf of regular functions over the open set . Note that the units of are the units of .

As an example, let be the projective line , then .

Another example is the following. Suppose that and let be given by with a separable polynomial of even positive degree and leading coefficient nonsquare in . Let the point above . Then .