  In this paper, we prove the generic version of Cantor spectrum for
quasi-periodic Schr\"{o}dinger operators with finitely smooth and small
potentials, and we also show pure point spectrum for a class of multi-frequency
$C^k$ long-range operators on $\ell^2(\Z^d)$. These results are based on
reducibility properties of finitely differentiable quasi-periodic $SL(2,\R)$
cocycles. More precisely, we prove that if the base frequency is Diophantine,
then a $C^k$ $SL(2,\R)$-valued cocycle is reducible if it is close to a
constant cocycle, sufficiently smooth and the rotation number of it is
Diophantine or rational with respect to the frequency.
