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The genuine stabilization of a $G$-topos

Banff International Research Station for Mathematical Innovation and Discovery

Let $G$ be a finite group and $X$ a topos with homotopy coherent $G$-action. From this, we construct a stable homotopy theory $Sp^G(X)$ which recovers and extends the theory of genuine $G$-spectra. We explain what our construction yields when: (i) $X$ is the topos of sheaves on a topological space with $G$-action (ii) $X$ is the etale $C_2$-topos of a scheme $S$ adjoined a square root of -1. This is a preliminary report on joint work with Elden Elmanto.

Mathematics; Algebraic topology; Category theory; homological algebra

video/mp4

Author affiliation: University of Notre Dame

2019-03-25

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69187

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/