Department of Mathematics - Master Calendar

The duality between an algebraic variety and its ring of regular functions is a cornerstone of algebraic geometry. To recover an algebraic stack with affine diagonal, however, one must pass one categorical level higher and consider its derived category of quasi-coherent sheaves. In general, Tannakian formalism has its limit - even derived categories fail to distinguish different stacks. In this talk, we will explain how richer layers of information can be encoded by successively passing to higher categorical structures. We will also introduce Stefanich rings, which may be viewed as commutative rings equipped with infinite deloopings of the multiplication. We will follow the notes Geometry and Higher Category Theory by Scholze.