  Let $\ell$ be a prime number different from the residue characteristic of a
non-archimedean local field $F$. We give formulations of $\ell$-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
$\ell$-adic coefficient field and the complex number field.
