Geometrization of the local Langlands correspondence, motivically

Abstract Based on the formalism of rigid-analytic motives of [J. Ayoub, M. Gallauer and A. Vezzani, The six-functor formalism for rigid analytic motives, Forum Math. Sigma 10 (2022), Paper no. e61], we extend our previous work [L. Fargues and P. Scholze, Geometrization of the local Langlands correspondence, preprint (2021), https://arxiv.org/abs/2102.134592021 ; to appear in Astérisque] from ℓ-adic sheaves to motivic sheaves. In particular, we prove independence of ℓ of the 𝐿-parameters constructed there.