  Let R be an integral domain of finite type over Z and let f:X --> Spec R be a
smooth projective morphism of relative dimension d >= 1. We investigate, for a
vector bundle E on the total space X, under what arithmetical properties of a
sequence (p_n, e_n)_{n \in \NN}, consisting of closed points p_n in Spec R and
Frobenius descent data E_{p_n} \cong F^{e_n}^*(F) on the closed fibers X_{p_n},
the bundle E_0 on the generic fiber X_0 is semistable.
