Let X be a smooth variety over $F_p$. Let E be a number field. For each
nonarchimedean place $\lambda$ of E prime to p consider the set of isomorphism
classes of irreducible lisse $\overline{E}_{\lambda}$-sheaves on X with
determinant of finite order such that for every closed point x in X the
characteristic polynomial of the Frobenius $F_x$ has coefficents in E. We prove
that this set does not depend on $\lambda$.

The idea is to use a method developed by G.~Wiesend to reduce the problem to
the case where X is a curve. This case was treated by L. Lafforgue.