Title: Tannakian formalism for stacks
Abstract: It is well known that the category of algebraic representations of an affine group scheme G over a field k is a k-linear abelian tensor category. Moreover, if k is algebraically
closed, then the group scheme G is completely determined by its category of representations. It then makes sense to ask which abelian tensor categories are equivalent to the representation category of an affine group scheme. In case k has characteristic zero, Deligne determined an internal characterisation of such categories: this is classical tannakian duality. Similarly, varieties, schemes, group schemes and various generalizations thereof are often studied via an associated symmetric monoidal Grothendieck category (the category of quasi-coherent sheaves or the category of representations). Lurie has shown that passage to quasi-coherent sheaves gives an embedding into the 2-category of symmetric monoidal Grothendieck categories for many algebro-geometric objects. Like before, it is natural to ask whether we can characterize the image of this embedding. In particular, one can ask which symmetric monoidal Grothendieck categories are equivalent to the category of quasi-coherent sheaves on an (Adams) stack. In this talk, I will give partial answers to these questions, both in positive characteristic and characteristic zero. I will not assume everyone knows what a stack is.
This is joint work with Kevin Coulembier.
Bregje Pauwels from the University of Sydney will be visiting and will give a talk in 1.33.
In person attendance is available for up to 25 people.
Virtual attendance via Zoom. To access the Zoom link please click here.