Apparaît dans la collection : Summer School on the Langlands Program

In the Langlands program over number fields, automorphic representations and Galois representations are placed into correspondence, using the cohomology of Shimura varieties as an intermediary. Over a function field, the appropriate intermediary is a moduli space of shtukas. We introduce the shtukas and their local analogues, which play a similar role in the local Langlands program. Along the way we construct the Fargues-Fontaine curve and discuss perfectoid spaces and diamonds. This survey may be seen as preparatory for the lectures of Fargues-Scholze.