2009/12/24 by Johannes Nicaise, Nicaise, Johannes, Julien Sebag +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation #math.AG
paper · pdf · doi:10.48550/arxiv.0912.4887
arxiv created 2009/12/24 · openalex publication_date 2009/12/24 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a quotient of the Grothendieck ring of varieties by identifying classes of universally homeomorphic varieties. We show that the standard realization morphisms factor through this quotient, and we argue that it is the correct value ring for the theory of motivic integration on formal schemes and rigid varieties in mixed characteristic. The present note is an excerpt of a detailed survey paper which will be published in the proceedings of the conference "Motivic integration and its interactions with model theory and non-archimedean geometry" (ICMS, 2008).