Jul 11 – 29, 2022
IHES
Europe/Paris timezone

Local Shtukas and the Langlands Program (2/2)

Jul 19, 2022, 9:20 AM
1h 20m
Marilyn and James Simons Conference Center (IHES)

Marilyn and James Simons Conference Center

IHES

35 route de Chartres, F-91440 Bures-sur-Yvette, France

Speaker

Prof. Jared WEINSTEIN (Boston Univ.)

Description

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 analogs, 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.

Presentation materials