Genuine-commutative structure on rational equivariant K-theory for finite abelian groups

Abstract

In this paper, the authors build on their previous work to show that periodic rational -equivariant topological -theory has a unique genuine-commutative ring structure for a finite abelian group. This means that every genuine-commutative ring spectrum whose homotopy groups are those of is weakly equivalent, as a genuine-commutative ring spectrum, to . In contrast, the connective rational equivariant -theory spectrum does not have this type of uniqueness of genuine-commutative ring structure.