ScalingStacks

This paper relies heavily on the work of Jacob Lurie, whom the authors thank for many helpful discussions and for his generosity in sharing his knowledge (and in particular for the suggestion of how to describe the higher $\mathcal{E}_{n}$-centers of $\qc(X)$ geometrically). DBZ and DN would like to thank Bertrand Toën for educating them in derived algebraic geometry and patiently explaining many arguments. They would also like to thank Victor Ostrik for sharing his understanding of Drinfeld centers and their applications to Hecke categories. JF thanks his advisor, Michael Hopkins, for discussions on the topological field theory aspects of this paper, as well as for his support and guidance. Many thanks to Andrew Blumberg and Amnon Neeman for detailed comments on early drafts. Finally, we would also like to thank the anonymous referees for their valuable feedback.

DBZ is partially supported by NSF CAREER grant DMS-0449830. JF was supported by an NSF Graduate Research Fellowship. DN is partially supported by NSF grant DMS-0600909 and a Sloan Research Fellowship. Work on this paper has taken place at the Aspen Center for Physics and the IAS (supported by NSF grant DMS-0635607), whom the authors thank for providing support and stimulating environments.