  A systematic ab-initio study within the framework of the local-spin-density
approximation including spin-orbit coupling and an orbital-polarization term is
performed for the spin and orbital moments and for the X-ray magnetic circular
dichroism (XMCD) spectra in hcp Co, in a Pt supported and a free standing Co
monolayer, and in a Pt supported and a free standing monatomic Co wire. When
including the orbital-polarization term, the orbital moments increase
drastically when going to lower dimensionality, and there is an increasing
asymmetry between the L_2 and L_3 XMCD signal. It is shown that spin and
orbital moments can be obtained with good accuracy from the XMCD spectra via
the sum rules. The <T_z> term of the spin sum rule is surprisingly small for
the wires, and the reason for this is discussed.
