Classifying perfect complexes of Z/2-Mackey functors - Clover May (NTNU, Norway)

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18th Meeting of "New directions in Group Theory and Triangulated Categories"

Date: October 7, 2021; Thursday.

Time: 3.30 pm UTC (4.30 pm UK time, 5.30 pm Berlin/Paris, 11.30 am NY time)

Speaker: Clover May (Norwegian University of Science and Technology)

Title: Classifying perfect complexes of Z/2-Mackey functors.

Abstract:
Mackey functors play a central role in equivariant homotopy theory, where homotopy groups are replaced by homotopy Mackey functors. In this talk, I will discuss joint work with Dan Dugger and Christy Hazel classifying perfect chain complexes of constant Mackey functors for G=\mathbb{Z}/2. Our decomposition leads to a computation of the Balmer spectrum of the derived category. We extend these results to classify all finite modules over the equivariant Eilenberg--MacLane spectrum H\underline{\mathbb{Z}/2}.