  Let $K$ be a $C_1$-field of any characteristic and $X$ a projective variety
over $K$. In this article we prove that for a finite Galois extension $L$ of
$K$, a simple sheaf with covering datum on $X \times_K L$ descends to a simple
sheaf on $X$. As a consequence, we show that there is a $1-1$ correspondence
between the set of geometrically stable sheaves on $X$ with fixed Hibert
polynomial $P$ and the set of $K$-rational points of the corresponding moduli
space.
