The local Langlands conjectures are certain conjectures in the context of the Langlands program. Where the genuine Langlands correspondence concerns global fields, the local Langlands correspondence concerns local fields.
The local Langlands conjectures assert a correspondence between representations of the Weil group? of a local field and representations of algebraic groups over the local field, generalizing local class field theory from abelian Galois groups to non-abelian Galois groups.
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