Equivariant motivic integration on formal schemes and the motivic zeta function

2015/11/27 by Annabelle Hartmann, Hartmann, Annabelle
Chemistry · Mathematics · #14D15 #14G22 #14L30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Axial and Atropisomeric Chirality Synthesis #FOS: Mathematics #math.AG #msc:14D15 #msc:14G22 #msc:14L30

paper · pdf · doi:10.48550/arxiv.1511.08656

40 pages

arxiv created 2015/11/27 · openalex publication_date 2015/11/27 · arxiv updated 2015/11/30 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

For a formal scheme over a complete discrete valuation ring with a good action of a finite group, we define equivariant motivic integration, and we prove a change of variable formula for that.To do so, we construct and examine an induced group action on the Greenberg scheme of such a formal scheme. Using this equivariant motivic integration, we define an equivariant volume Poincaré series, from which we deduce Denef and Loeser's motivic zeta function including the action of the profinite group of roots of unity.

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