Sheaf Models in Rational Stable Equivariant Homotopy 🌀

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 rudradipbiswas@gmail.com.

More details about this seminar series are here -
https://sites.google.com/view/ndgttc/home
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44th Meeting of "New Directions in Group Theory and Triangulated Categories"

Date: June 28, 2022; Tuesday.

Time: 4 pm UK

Speaker: David Barnes (Queen's University Belfast)

Title: Sheaf models for rational stable equivariant homotopy theory

Abstract: Sheaves sit at an interface of algebra and geometry. Equivariant sheaves offer even more structure, allowing for different group actions at different stalks. We are interested in the case where both the base space and group of equivariance are profinite (that is, compact, Hausdorff and totally disconnected). This combination provides many useful consequences, such as a good notion of equivariant presheaves and an explicit construction of infinite products.

The 2019 PhD thesis of Sugrue used equivariant sheaves to give an algebraic model for rational G-equivariant stable homotopy theory, where G is profinite. In this talk I will explain the model and related results, such as the equivalence between equivariant sheaves and rational Mackey functors (for profinite G).