Naive-commutative structure on rational equivariant $K$-theory for abelian groups

Anna Marie Bohmann; Christy Hazel; Jocelyne Ishak; Magdalena Kędziorek; Clover May

doi:10.1016/j.topol.2022.108100

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arXiv · 2002.01556

Naive-commutative structure on rational equivariant $K$-theory for abelian groups

Anna Marie Bohmann·Christy Hazel·Jocelyne Ishak·Magdalena Kędziorek·Clover May

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Abstract

In this paper, we calculate the image of the connective and periodic rational equivariant complex $K$-theory spectrum in the algebraic model for naive-commutative ring $G$-spectra given by Barnes, Greenlees and K\k{e}dziorek for finite abelian $G$. Our calculations show that these spectra are unique as naive-commutative ring spectra in the sense that they are determined up to weak equivalence by their homotopy groups. We further deduce a structure theorem for module spectra over rational equivariant complex $K$-theory.

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Anna Marie Bohmann, Christy Hazel, Jocelyne Ishak, Magdalena Kędziorek, Clover May. 2020-02-04. Naive-commutative structure on rational equivariant $K$-theory for abelian groups. https://doi.org/10.1016/j.topol.2022.108100

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