  Let X be an algebraic curve. We study the problem of parametrizing geometric
data over X, which is only generically defined. E.g., parametrizing generically
defined (aka rational) maps from X to a fixed target scheme Y. There are three
methods for constructing functors of points for such moduli problems (all
originally due to Drinfeld), and we show that the resulting functors are
equivalent in the fppf Grothendieck topology. As an application, we obtain
three presentations for the category of D-modules "on" B (K) \G (A) /G (O), and
we combine results about this category coming from the different presentations.

Representation Theory;Algebraic Geometry