Connected components of the moduli space of L-parameters

There have been several recent approaches to defining a moduli space of L-parameters over Z[1/p], in order to obtain refined versions of the local Langlands conjecture ``at all primes away from p at once''. The components of this space are expected to be closely related to blocks in the category of smooth Z[1/p]-representations of a p-adic group. DHKM gave a conjectural description of these components, and I will explain a generalization and proof of this conjecture.