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Endomorphisms of Equivariant Algebraic $K$-theory

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arxiv 2304.02544 v2 pith:B65IDYUH submitted 2023-04-05 math.AG math.ATmath.KT

K. Arun Kumar , Girja S Tripathi This is my paper · ORCID
classification math.AGmath.ATmath.KT
keywords equivariantendomorphismsgrassmanniansmotivictheoryalgebraiccategoryhomotopy
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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 $K_0(G,-)$ coincides with the set of endomorphisms of infinite Grassmannians in the equivariant motivic homotopy category by explicitly computing the equivariant $K$-theory of Grassmannians.

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