• Corpus ID: 232068965

Geometrization of the local Langlands correspondence

@inproceedings{Fargues2016GeometrizationOT,
  title={Geometrization of the local Langlands correspondence},
  author={Laurent Fargues and Peter Scholze},
  year={2016}
}
Following the idea of [Far16], we develop the foundations of the geometric Langlands program on the Fargues--Fontaine curve. In particular, we define a category of $\ell$-adic sheaves on the stack $\mathrm{Bun}_G$ of $G$-bundles on the Fargues--Fontaine curve, prove a geometric Satake equivalence over the Fargues--Fontaine curve, and study the stack of $L$-parameters. As applications, we prove finiteness results for the cohomology of local Shimura varieties and general moduli spaces of local… 

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