  It is known that a vector bundle E on a smooth projective curve Y defined
over an algebraically closed field is semistable if and only if there is a
vector bundle F on Y such that the cohomologies of E\otimes F vanish. We extend
this criterion for semistability to vector bundles on curves defined over
perfect fields. Let X be a geometrically irreducible smooth projective curve
defined over a perfect field k, and let E be a vector bundle on X. We prove
that E is semistable if and only if there is a vector bundle F on $X$ such that
the cohomologies of E\otimes F vanish. We also give an explicit bound for the
rank of $F$.
