Global model categories and topological André-Quillen cohomology

Abstract

We introduce global model categories as a general framework to capture several phenomena in global equivariant homotopy theory. We then construct genuine stabilizations of these, generalizing the usual passage from unstable to stable global homotopy theory. Finally, we define the global topological André-Quillen cohomology of an ultra-commutative ring spectrum and express it in terms of a genuine stabilization in our framework in analogy with the classical non-equivariant description obtained by Basterra and Mandell.

Revision following a referee report: new subsection on equivariant TAQ, various minor corrections and improvements to exposition. 79 pages