local Langlands conjecture

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.

Part of the above material is taken from

- Wikipedia,
*Local Langlands conjectures*.

See also

- Colin Bushnell, Guy Henniart,
*The local Langlands conjecture for $GL(2)$*.

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Revised on August 24, 2014 03:59:32
by Urs Schreiber
(89.15.239.211)