Global orthogonal spectra

For any finite group G, there are several well-established definitions of a G-equivariant spectrum. In this paper, we develop the definition of a global orthogonal spectrum. Loosely speaking, this is a coherent choice of orthogonal G-spectrum for each finite group G. We use the framework of enriched indexed categories to make this precise. We also consider equivariant K-theory and Spin^c-cobordism from this perspective, and we show that the Atiyah--Bott--Shapiro orientation extends to the global context.Comment: 17 page

Graded Tambara Functors

We define the notion of an $\mathcal{RO}(G)$-graded Tambara functor and prove that any $G$-spectrum with norm multiplication gives rise to such an $\mathcal{RO}(G)$-graded Tambara functor.Comment: 25 pages; elaborated on the description of graded Tambara functors and clarified some of the category theory. Added more detailed reference

A Presheaf Interpretation of the Generalized Freyd Conjecture

We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new results, but at least one known example drops out quite trivially.Comment: 8 pages; formerly titled "Thinking about the Freyd conjecture