Abstract

Many ring-like structures come with the notion of prime ideals which assemble into a topological space. Tambara functors for a finite group G are no exception to this rule. Nakaoka defined the notion of the prime spectrum of a Tambara functor, which has since been computed in several examples of interest. Tambara functors are at an extreme of a family of structures where we ask for the existence of all additive transfers and multiplicative norms.  There is a methodical way to remove this structure via the concept of bi-incomplete Tambara functors, which retrieves the notions of Green functors and coefficient systems along the way. By altering Nakaoka’s definition one can begin to explore the prime spectrum for bi-incomplete Tambara functors. In this talk I will report on some structural and computational results in this direction. This is joint work with Ben Spitz and J.D. Quigley.