We aim at reproducing the mass- and sigma-[alpha/Fe] relations in the stellar populations of early-type galaxies by means of a cosmologically motivated assembly history for the spheroids. We implement a detailed treatment for the chemical evolution of H, He, O and Fe in GalICS, a semi-analytical model for galaxy formation which successfully reproduces basic low- and high-redshift galaxy properties. The contribution of supernovae (both type Ia and II) as well as low- and intermediate-mass stars to chemical feedback are taken into account. We find that this chemically improved GalICS does not produce the observed mass- and sigma-[alpha/Fe] relations. The slope is too shallow and scatter too large, in particular in the low and intermediate mass range. The model shows significant improvement at the highest masses and velocity dispersions, where the predicted [alpha/Fe] ratios are now marginally consistent with observed values. We show that this result comes from the implementation of AGN (plus halo) quenching of the star formation in massive haloes. A thorough exploration of the parameter space shows that the failure of reproducing the mass- and sigma-[alpha/Fe] relations can partly be attributed to the way in which star formation and feedback are currently modelled. The merger process is responsible for a part of the scatter. We suggest that the next generation of semi-analytical model should feature feedback (either stellar of from AGN) mechanisms linked to single galaxies and not only to the halo, especially in the low and intermediate mass range. The integral star formation history of a single galaxy determines its final stellar [alpha/Fe] as it might be expected from the results of closed box chemical evolution models. (abridged)
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