Geometrization of the local Langlands correspondence, motivically

Based on the formalism of rigid-analytic motives of Ayoub–Gallauer–Vezzani, we extend our previous work with Fargues from $\mathrm{\ell }$-adic sheaves to motivic sheaves. In particular, we prove independence of $\mathrm{\ell }$ of the $L$-parameters constructed there.