Connected components of the moduli space of L-parameters

Recently, in order to formulate a categorical version of the local Langlands correspondence, several authors (Dat--Helm--Kurinczuk--Moss, Fargues--Scholze, Zhu, ...) have defined algebraic moduli spaces of L-parameters over the ring Z[1/p], where p is a prime number. Via categorical local Langlands, the connected components of these spaces are expected to be closely related to the blocks in the category of smooth Z[1/p]-representations of a p-adic group G, which in turn encode information about congruences between smooth C-representations of G. Dat--Helm--Kurinczuk--Moss gave a conjectural description of these connected components, and I will describe a generalization and proof of this conjecture.