Abstract: 

Let F be a non-archimedean local field. I will explicitly describe:4

(1) (The category of quasicoherent sheaves on) The connected component of the moduli space of Langlands parameters over Z_l-bar containing an irreducible tame L-parameter with $F_l-bar$ coefficients;
(2) the block of the category of smooth representations of $G(F)$ with $Z_l-bar$ coefficients containing a depth-zero supercuspidal representation with $F_l-bar$ coefficients.


The argument works at least for (simply connected) split reductive group $G$, but I will focus on the example of $GL_2$ for simplicity. The two sides turn out to match abstractly. If time permits, I will explain how to get the categorical local Langlands correspondence for depth-zero supercuspidal part of $GL_2$ with $Z_l-bar$ coefficients in Fargues-Scholze's form.