Endomorphisms of Equivariant Algebraic K-theory

2023/04/05 by K. Arun Kumar, Kumar, K. Arun, Girja S Tripathi +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2304.02544

openalex publication_date 2023/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for the action of a finite constant group scheme, equivariant algebraic K-theory is represented by a colimit of Grassmannians in the equivariant motivic homotopy category. Using this result we show that the set of endomorphisms of the equivariant motivic space defined by K₀(G,-) coincides with the set of endomorphisms of infinite Grassmannians in the equivariant motivic homotopy category by explicitly computing the equivariant K-theory of Grassmannians.

Related

• Equivariant Motivic Homotopy Theory
• Motivic homotopy theory of group scheme actions
• Equivariant Algebraic K-Theory and Derived completions II: the case of Equivariant Homotopy K-Theory and Equivariant K-Theory
• Motivic homotopy of group scheme actions
• Algebraic K-theory of quotient stacks