### On the local Langlands correspondence mod ell, by Chandrashekhar Khare

We prove that the reduction mod \ell of the local Langlands
correspondence between supercuspidal representations
of GL_n(F), where F is a finite extension of Q_p,
and representations of the Galois group of F is well-defined.
The results and methods of this paper have been used by Vigneras
to give a proof of the ``local Langlands conjecture
mod \ell'', that was proved earlier by her by different methods
(local harmonic analysis mod \ell) for \ell>n. Unlike
the local methods used earlier by Vigneras, our
more global method also generalises well to
the characteristic p case.

Chandrashekhar Khare <shekhar@math.tifr.res.in>