Title: Local-global compatibility over function fields Abstract: We show that V. Lafforgue's global Langlands correspondence is compatible with Fargues–Scholze's semisimplified local Langlands correspondence. As a result, we canonically lift Fargues–Scholze's construction to a non-semisimplified local Langlands correspondence for fields of characteristic ≥ 5. We also deduce that Fargues–Scholze's construction agrees with that of Genestier–Lafforgue, answering a question of Fargues–Scholze, Hansen, […]