The tensor triangular geometry of functor categories

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• Gregory Arone (Stockholm University)
• Tuesday 20 May 2025, 14:00-15:00
• Seminar Room 2, Newton Institute.

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EHT - Equivariant homotopy theory in context

We consider the (infinity) category of excisive (aka polynomial) functors from Spectra to Spectra. Understanding this category is a basic problem in functor calculus. We will approach it from the perspective of tensor triangular geometry. Day convolution equips the category of excisive functors with the structure of a rigid monoidal triangulated category. We describe completely the Balmer spectrum of this category, i.e., its spectrum of prime tensor ideals. This leads to a Thick Subcategory Theorem for excisive functors. There is a rather far-reaching analogy between the category of excisive functors and the category of G-spectra that informs this project. Joint with Tobi Barthel, Drew Heard and Beren Sanders.

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

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