Tannakian Formalism for Stacks

Explore the intricacies of Tannakian formalism for stacks in this 53-minute lecture presented by Bregje Pauwels of Macquarie University at IPAM's Symmetric Tensor Categories and Representation Theory Workshop. Delve into the relationship between affine group schemes and their representation categories, examining Deligne's characterization of abelian tensor categories in characteristic zero fields. Investigate the embedding of algebro-geometric objects into symmetric monoidal Grothendieck categories, as demonstrated by Lurie. Analyze the challenges of characterizing categories equivalent to quasi-coherent sheaves on stacks. Discover recent developments in both positive and zero characteristic cases, based on joint work with Kevin Coulembier. Gain insights into classical Tannaka duality and its extensions to more general algebraic structures.