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Gregory Arone (Stockholm University)
Tuesday 20 May 2025, 15:30-16:30
The tensor triangular geometry of functor categories
- 👤 Speaker: Gregory Arone (Stockholm University)
- 📅 Date & Time: Tuesday 20 May 2025, 15:30 - 16:30
- 📍 Venue: Seminar Room 2, Newton Institute
Abstract
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.
Series This talk is part of the Isaac Newton Institute Seminar Series series.
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