Chirantan Chowdhury: Abstract Six-Functor Formalisms and Motivic Homotopy Theory of Algebraic Stacks

Abstract:

The Grothendieck six-functor formalism has been one of the key features in the language of motivic homotopy theory. Thanks to the work of Ayoub, Cisinski, Déglise, Hoyois, and many others, the theory of motivic six-functors on schemes is now well established. The natural follow-up question is: Can we extend this formalism to a larger class of geometric objects like algebraic stacks? In this talk, we explain how one can extend the formalism of motivic homotopy theory to algebraic stacks as recently developed by Chowdhury and Khan-Ravi. Such an extension involves the theory of abstract six-functor formalisms developed by Liu–Zheng and Mann. We shall address the results regarding the properties of these six functors (joint work with Alessandro D'Angelo). If time permits, we shall discuss some possible applications in motivic Langlands.