  Let f : X --> Spec(Z) be an arithmetic variety of dimension d >= 2 and (H, k)
an arithmetically ample Hermitian line bundle on X. Let (E, h) be a rank r
vector bundle on X. In this paper, we will prove that if E is semistable with
respect to H on each connected component of the infinite fiber of X, then
  { c_2(E, h) - (r-1)/(2r) c_1(E, h)^2 } c_1(H, k)^{d-2} >= 0. Moreover, if the
equality of the above inequality holds, then E is projectively flat and h is a
weakly Einstein-Hermitian metric.
