On algebraic spaces with an action of G_m

2013/08/12 by Drinfeld, Vladimir · 1 citation
#20G05 #22E57 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14L30 #Representation Theory (math.RT) #Secondary 14D24

paper · doi:10.48550/arxiv.1308.2604

Abstract

Let Z be an algebraic space of finite type over a field, equipped with an action of the multiplicative group G_m. In this situation we define and study a certain algebraic space equipped with an unramified morphism to A¹× Z× Z, where A¹ is the affine line. (If Z is affine and smooth this is just the closure of the graph of the action map G_m× Z→ Z.) In articles joint with D.Gaitsgory we use this set-up to prove a new result in the geometric theory of automorphic forms and to give a new proof of a very important theorem of T. Braden.

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