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$D$-modules on spaces of rational maps

Published online by Cambridge University Press:  31 March 2014

Jonathan Barlev
Affiliation:
Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637, USA email jonathan.barlev@math.uchicago.edu
Corresponding
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Abstract

Let $X$ be an algebraic curve. We study the problem of parametrizing geometric structures over $X$ which are only generically defined. For example, parametrizing generically defined maps (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’ $B(K)\backslash G(\mathbb{A})/G(\mathbb{O})$, and we combine results about this category coming from the different presentations.

MSC classification

Type
Research Article
Copyright
© The Author 2014 

References

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