# Colloquium: Zev Rosengarten (HUJI) - Moduli Spaces of Morphisms Into Algebraic Groups

Date:
Thu, 14/10/202114:30-15:30

Title: Moduli Spaces of Morphisms Into Algebraic Groups

Abstract: For a pair of (quasi-projective) varieties X and Y over some field k, the functor Mor(X, Y) of morphisms from X to Y is representable when X is projective. If one relaxes the projectivity assumption on X (say, if X is affine), this usually fails completely. Nevertheless, we will show that, in great generality, this moduli space is representable in a suitable sense when Y is a solvable algebraic group, with special emphasis on the case in which k is imperfect and Y is (wound) unipotent. As an application, we will show that one of the main results of geometric class field theory remains true after base change by a geometrically reduced variety. All of the important concepts will be introduced in the talk, with minimal background knowledge required.