Prime spectra of bi-incomplete Tambara functors

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• Scott Balchin (Queen's University Belfast)
• Thursday 15 May 2025, 14:00-15:00
• Seminar Room 1, Newton Institute.

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EHTW03 - New horizons for equivariance in homotopy theory

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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