A categorical approach to the stable center conjecture

Understand

The stable center conjecture asserts that the space of stable distributions in the Bernstein center of a reductive p-adic is closed under convolution.

• It is closely related to the notion of an L-packet and endoscopy theory.
• We describe a categorical approach to the depth zero part of the conjecture.
• As an illustration of our method, we show that the Bernstein projector to the depth zero spectrum is stable.