The quotient map on the equivariant Grothendieck ring of varieties

Speaker: Annabelle Hartmann (Bonn)

Date, time & place: January 21, 2016, 10:15 am, WSC-N-U-3.05

Title:  The quotient map on the equivariant Grothendieck ring of varieties

Abstract:  The aim of the talk will be to explain the existence of a well defined quotient map on the $G$-equivariant Grothendieck ring of varieties for an abelian finite group $G$.
The main problem here is to compute the class of a quotient of an affine bundle with affine $G$-actions in the Grothendieck ring. I will explain why such a class only depends on the rank and the base of the bundle. Moreover, I will consider the problems arising in the case of wild group actions. Here one has to work in a modified Grothendieck ring to be able to handle purely inseparable maps.
As an application, I will use my result to compute the quotient of the nearby fiber using motivic integration with Galois actions. If time permits, I will also comment on the analogue construction for formal schemes.