Abstract
Let F be a p-adic field. We will prove that the local Langlands conjecture between the supercuspidal irreducible Q ℓ -representations of GL( n, F) and the irreducible Q ℓ -representations of dimension n of the Weil group W F is compatible with the reduction modulo ℓ when ℓ≠ p,ℓ> n.
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