Derived structures in the Langlands Correspondence

Abstract

We survey several recent examples of derived structures emerging in connection with the Langlands correspondence. Cases studies include derived Galois deformation rings, derived Hecke algebras, derived Hitchin stacks, and derived special cycles. We also highlight some open problems that we expect to be important for future progress.

Many minor changes and corrections. To appear in the proceedings of the 2022 IHES summer school