Local Langlands correspondences in ℓ-adic coefficients

Abstract

Let ℓ be a prime number different from the residue characteristic of a non-archimedean local field F. We give formulations of ℓ-adic local Langlands correspondences for connected reductive algebraic groups over F, which we conjecture to be independent of a choice of an isomorphism between the ℓ-adic coefficient field and the complex number field.