TOPICS
Search

Drinfeld Ring


Let C be a smooth geometrically connected projective curve over F_q with q=p^s a prime power. Let infty be a fixed closed point of X but not necessarily F_q-rational. A Drinfeld ring is the ring A=Gamma(C-{infty},O_C), i.e., the sections of the sheaf OC of regular functions over the open set C-{infty}. Note that the units of A are the units of F_q.

As an example, let C be the projective line P^1/F_q, then A=F_q[T].

Another example is the following. Suppose that p!=2 and let C be given by Y^2=f(X) with f(X) a separable polynomial of even positive degree and leading coefficient nonsquare in F_q. Let infty the point above X=infty. Then A=F_q[X,Y].


See also

Drinfeld Module

This entry contributed by José Gallardo Alberni

Explore with Wolfram|Alpha

References

Gekeler, E.-U. "Drinfeld Modules and Local Fields of Positive Characteristic." §2.4 in Geometry and Topology Monographs, Vol. 3: Invitation to Higher Local Fields. pp. 239-253. http://www.maths.warwick.ac.uk/gt/gtmono.html.

Referenced on Wolfram|Alpha

Drinfeld Ring

Cite this as:

Alberni, José Gallardo. "Drinfeld Ring." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/DrinfeldRing.html

Subject classifications