Séminaire de Mathématique

The mod-p Local Langlands Program and Hecke Modules

by Prof. Karol KOZIOL (IPDE, IHÉS)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

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Abstract: The mod-p Local Langlands Program aims to find a relationship between the mod-p representation theory of p-adic reductive groups and Galois groups, in the spirit of the classical Langlands correspondence on complex vector spaces.  I'll describe several aspects of this theory, and outline how techniques from the classical case fail in the mod-p setting.  Finally, I'll describe how modules over certain Hecke algebras can be used as an avatar for this correspondence in certain situations.