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A systematic ab-initio study within the framework of the local-spin-densityapproximation including spin-orbit coupling and an orbital-polarization term isperformed for the spin and orbital moments and for the X-ray magnetic circulardichroism (XMCD) spectra in hcp Co, in a Pt supported and a free standing Comonolayer, and in a Pt supported and a free standing monatomic Co wire. Whenincluding the orbital-polarization term, the orbital moments increasedrastically when going to lower dimensionality, and there is an increasingasymmetry between the L_2 and L_3 XMCD signal. It is shown that spin andorbital moments can be obtained with good accuracy from the XMCD spectra viathe sum rules. The <T_z> term of the spin sum rule is surprisingly small forthe wires, and the reason for this is discussed

From the bulk to monatomic wires: Anab initiostudy of magnetism in Co systems with various dimensionality