D-modules on Spaces of Rational Maps and On Other Generic Data
Contributors: Gaitsgory, Dennis; Avni, Nir; Lurie, Jacob
Published: 2012
Language: eng
Description: 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) \G (A) /G (O) and combine results about this category coming from the different presentations.
Notes: Keywords: D-modules, generic data, Geometric Langlands, Homologically contractible.

Thesis Ph.D. Harvard University 2012