Arbeitsgemeinschaft: The Geometric Langlands Conjecture

  • Laurent Fargues

    Université de Paris VI, France
  • Dennis Gaitsgory

    Harvard University, Cambridge, USA
  • Peter Scholze

    Universität Bonn, Germany
  • Kari Vilonen

    Northwestern University, Evanston, USA
Arbeitsgemeinschaft: The Geometric Langlands Conjecture cover
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The Langlands program is a vast, loosely connected, collection of theorems and conjectures. At quite different ends, there is the geometric Langlands program, which deals with perverse sheaves on the stack of -bundles on a smooth projective curve, and the local Langlands program over -adic fields, which deals with the representation theory of -adic groups. Recently, inspired by applications to p-adic Hodge theory, Fargues and Fontaine have associated with any -adic field an object that behaves like a smooth projective curve. Fargues then suggested that one can interpret the geometric Langlands conjecture on this curve, to give a new approach towards the local Langlands program over -adic fields.

Cite this article

Laurent Fargues, Dennis Gaitsgory, Peter Scholze, Kari Vilonen, Arbeitsgemeinschaft: The Geometric Langlands Conjecture. Oberwolfach Rep. 13 (2016), no. 2, pp. 1027–1098

DOI 10.4171/OWR/2016/20