Some remarks on vector bundles

Let X be a smooth projective variety over an algebraically closed field k of characteristic p> 0, F: X → X the absolute Frobenius morphism, fix an ample line bundle H on X. If V is a vector bundle, then we will say that V is Frobenius stable (resp. frobenius semi-stable) with respect to H if V and F ∗(V) are stabl