This is a recorded version of the following talk from our "New Directions in Group Theory and Triangulated Categories" series. To receive updates about this series, or to suggest speakers (including yourself), please email me at [email protected].

More details about this seminar series are here -
https://sites.google.com/view/ndgttc/...
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90th Meeting of "New Directions in Group Theory and Triangulated Categories"

Date: March 14, 2024; Thursday

Time: 4 pm UK

Speaker: Gregory Arone (Stockholm University)

Title: The tensor triangular geometry of functor categories

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. A key ingredient in the proof is a blueshift theorem for the generalized Tate construction associated with the family of non-transitive subgroups of products of symmetric groups. If there is time, I will say something about work in progress to extend these results to more general functor categories. Joint with Tobias Barthel, Drew Heard, and Beren Sanders.