2014/08/31 by Annabelle Hartmann · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Abelian group #Algebra over a field #Algebraic Geometry and Number Theory #Equivariant map #Grothendieck group #Invariant (physics) #Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Pure mathematics #Quotient #Ring (chemistry) #math.AG
paper · pdf · doi:10.1007/s00229-016-0842-2
published in manuscripta mathematica 151(3-4), 419-451 (Springer Science+Business Media) · 28 pages; minor changes; to appear in Manuscripta Mathematica. The final publication is available at Springer via http://dx.doi.org/[10.1007/s00229-016-0842-2]
arxiv created 2016/03/31 · arxiv updated 2016/04/01 · openalex publication_date 2016/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.