Tannakian reconstruction in derived algebraic geometry

Abstract

We prove analogues of Tannakian reconstruction theorems of Lurie and Bhatt--Halpern-Leistner in \emph{derived} algebraic geometry, where the basic geometric objects are spectra of animated rings rather than ${\mathbb{E}}_{\infty }$-rings. In this setting, symmetric monoidal $\infty$-categories are replaced by the $\hat{I}˜$-categories of Nuiten--Toën. These are enhancements of symmetric monoidal $\infty$-categories which capture the strict commutativity structure on animated rings.

34 pages. Comments welcome!