Naive-commutative ring structure on rational equivariant \(K\)-theory for abelian groups (Q2145892)

It has been an ongoing project by Greenlees, Shipley and coauthors to provide algebraic models for variants of \(G\)-equivariant rational spectra via zig-zags of Quillen equivalences. This paper is concerned with \(\mathrm{Comm}(\mathcal{A}(G)_\mathbb{Q})\), the algebraic model for naive-commutative spectra for a finite abelian group \(G\). Unlike in the non-equivariant setting, there are multiple kinds of commutativity: naive commutativity is the least ``structured'' of them and corresponds to the absence of multiplicative norm maps. The authors explicitly describe the image of \(KU^G_\mathbb{Q}\) and of \(KU^G_\mathbb{Q}\)-module spectra in \(\mathrm{Comm}(\mathcal{A}(G)_\mathbb{Q})\) and discuss properties of the image of \(ku^G_\mathbb{Q}\), thus paving the way for future concrete calculations and applications.