• Corpus ID: 232068965

Geometrization of the local Langlands correspondence

  title={Geometrization of the local Langlands correspondence},
  author={Laurent Fargues and Peter Scholze},
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… 

$p$-adic sheaves on classifying stacks, and the $p$-adic Jacquet-Langlands correspondence

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Les zéros des fonctions analytiques d’une variable sur un corps valué complet

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Vector bundles and p-adic Galois representations. In Fifth International Congress of Chinese Mathematicians. Part 1, 2, volume 2 of AMS/IP Stud

  • Adv. Math., 51,
  • 2012