Algebraic K-theory and Grothendieck-Witt theory of monoid schemes

2020/09/26 by Jens Niklas Eberhardt, Oliver Lorscheid, Eberhardt, Jens Niklas +3
Mathematics · #19D10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2009.12636

openalex publication_date 2020/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the algebraic K-theory and Grothendieck-Witt theory of proto-exact categories of vector bundles over monoid schemes. Our main results are the complete description of the algebraic K-theory space of an integral monoid scheme X in terms of its Picard group Pic(X) and pointed monoid of regular functions Γ(X, O_X) and a description of the Grothendieck-Witt space of X in terms of an additional involution on Pic(X). We also prove space-level projective bundle formulae in both settings.

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