# D-Modules on Spaces of Rational Maps and on Other Generic Data

 Title: D-Modules on Spaces of Rational Maps and on Other Generic Data Author: Barlev, Jonathan Citation: Barlev, Jonathan. 2012. D-Modules on Spaces of Rational Maps and on Other Generic Data. Doctoral dissertation, Harvard University. Full Text & Related Files: Barlev_gsas.harvard_0084L_10134.pdf (1.249Mb; PDF) Abstract: Fix an algebraic curve X. We study the problem of parametrizing geometric data over X, which is only generically deﬁned. E.g., parametrizing generically deﬁned 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 combine results about this category coming from the different presentations. Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10056540 Downloads of this work: