2015/05/28 by Mona Merling, Merling, Mona · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1505.07562
openalex publication_date 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A group action on the input ring or category induces an action on the algebraic K-theory spectrum. However, a shortcoming of this naive approach to equivariant algebraic K-theory is, for example, that the map of spectra with G-action induced by a G-map of G-rings is not equivariant. We define a version of equivariant algebraic K-theory which encodes a group action on the input in a functorial way to produce a genuine algebraic K-theory G-spectrum for a finite group G. The main technical work lies in studying coherent actions on the input category. A payoff of our approach is that it builds a unifying framework for equivariant topological K-theory, Atiyah's Real K-theory, and existing statements about algebraic K-theory spectra with G-action. We recover the map from the Quillen-Lichtenbaum conjecture and the representational assembly map studied by Carlsson and interpret them from the perspective of equivariant stable homotopy theory.