D-modules on Spaces of Rational Maps and on other Generic Data

Details D-modules on Spaces of Rational Maps and on other Generic Data D-modules on Spaces of Rational Maps and on other Generic Data

2012-04-16

arxiv.org/abs/1204.3469v1

Mathematics

Representation Theory

55 pages

Scientific paper

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.

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