THE l-MODULAR LOCAL LANGLANDS CORRESPONDENCE AND LOCAL CONSTANTS

Let F be a non-archimedean local field of residual characteristic p, l not equal p be a prime number, and W-F the Weil group of F. We classify equivalence classes of W-F-semisimple Deligne l-modular representations of W-F in terms of irreducible l-modular representations of W-F, and extend constructions of Artin-Deligne local constants to this setting. Finally, we define a variant of the l-modular local Langlands correspondence which satisfies a preservation of local constants statement for pairs of generic representations.