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Motivic measures and \mathbbF1-geometries

2019/01/29 by Lieven Le Bruyn, Bruyn, Lieven Le
Chemistry · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Chemistry #Combinatorics #Discrete mathematics #FOS: Mathematics #Functor #Homotopy and Cohomology in Algebraic Topology #Lambda #Mathematics #Physics #Pure mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Ring (chemistry) #Rings and Algebras (math.RA) #Subring #math.AG #math.QA #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.1901.10243

arxiv created 2019/01/29 · openalex publication_date 2019/01/29 · arxiv updated 2019/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Right adjoints for the forgetful functors on λ-rings and bi-rings are applied to motivic measures and their zeta functions on the Grothendieck ring of \mathbbF1-varieties in the sense of Lorscheid and Lopez-Pena (torified schemes). This leads us to a specific subring of \mathbbW(ℤ), properly containing Almkvist's ring \mathbbW0(ℤ), which might be a natural receptacle for all local factors of completed zeta functions.

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