English

Endomorphisms of Equivariant Algebraic $K$-theory

Algebraic Geometry 2025-08-15 v2 Algebraic Topology K-Theory and Homology

Abstract

We prove that for the action of a finite constant group scheme, equivariant algebraic KK-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,)K_0(G,-) coincides with the set of endomorphisms of infinite Grassmannians in the equivariant motivic homotopy category by explicitly computing the equivariant KK-theory of Grassmannians.

Keywords

Cite

@article{arxiv.2304.02544,
  title  = {Endomorphisms of Equivariant Algebraic $K$-theory},
  author = {K. Arun Kumar and Girja S Tripathi},
  journal= {arXiv preprint arXiv:2304.02544},
  year   = {2025}
}

Comments

20 pages; substantially revised, version accepted for publication

R2 v1 2026-06-28T09:51:13.306Z