  Let X be a smooth curve over a finite field of characteristic p, let l be a
prime number different from p, and let L be an irreducible lisse l-adic sheaf
on X whose determinant is of finite order.
  By a theorem of Lafforgue, for each prime number l' different from p, there
exists an irreducible lisse l'-adic sheaf L' on X which is compatible with L,
in the sense that at every closed point x of X, the characteristic polynomials
of Frobenius at x for L and L' are equal.
  We prove an "independence of l" assertion on the fields of definition of
these irreducible l'-adic sheaves L' : namely, that there exists a number field
F such that for any prime number l' different from p, the l'-adic sheaf L'
above is defined over the completion of F at one of its l'-adic places.
