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The quotient map on the equivariant Grothendieck ring of varieties

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Annabelle Hartmann - SFB-Transregio-45-Seminar zur Algebraischen Geometrie

  • Seminar
When Dec 15, 2015
from 02:00 pm to 04:00 pm
Where Bonn, Raum 0.011, Mathematik-Zentrum, Endenicher Allee 60
Contact Name Sachinidis
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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, which is using equivariant motivic integration on formal schemes.

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