  We generalize the work of M. Harris and R. Taylor on the local Langlands
correspondence for the linear group over $\mathbb{Q}_p$. We prove some cases of
the Kottwitz conjectures for the supercuspidal part of the compactly supported
$\ell$-adic cohomology of Rapoport-Zink rigid-analytic spaces. This means that
we decompose this part in terms of local Langlands correspondences.
  In particular, we prove the first case of a non-abelian reciprocity law
constructed geometrically and associated to groups other than inner forms of
the linear group. More precisely, we do this for the unramified unitary group
in three variables over $\mathbb{Q}_p$.
