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manuscripta mathematica

, Volume 151, Issue 3–4, pp 419–451 | Cite as

The quotient map on the equivariant Grothendieck ring of varieties

  • Annabelle HartmannEmail author
Article

Abstract

For a scheme S with a good action of a finite abelian group G having enough roots of unity we show that the quotient map on the G-equivariant Grothendieck ring of varieties over S is well defined with image in the Grothendieck ring of varieties over S/G in the tame case, and in the modified Grothendieck ring in the wild case. To prove this we use a result on the class of the quotient of a vector space by a quasi-linear action in the Grothendieck ring of varieties due to Esnault and Viehweg, which we also generalize to the case of wild actions. As an application we deduce that the quotient of the motivic nearby fiber is a well defined invariant.

Mathematics Subject Classification

Primary 14L30 Secondary 14R10 14E08 14C15 

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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Universität BonnBonnGermany

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