  The main tool in Ng\^o Bao Ch\^au's proof of the Langlands-Shelstad
fundamental lemma, is a theorem on the support of the relative cohomology of
the elliptic part of the Hitchin fibration. For GL(n) and a divisor of degree
>2g-2, the theorem says that the relative cohomology is completely determined
by its restriction to any dense open subset of the base of the Hitchin
fibration. In this note we would like to present in this particular case, our
extension of that theorem to the whole Hitchin fibration, including the global
nilpotent cone.
