We study the impact of the environment on the evolution of galaxies in the zCOSMOS 10k sample in the redshift range 0.1<z<1.0 over an area of ~1.5 deg2. The considered sample of secure spectroscopic redshifts contains about 8500 galaxies, with their stellar masses estimated by SED fitting of the multiwavelength optical to NIR photometry. The evolution of the galaxy stellar mass function (GSMF) in high and low density regions provides a tool to study the mass assembly evolution in different environments; moreover, the contributions to the GSMF from different galaxy types, as defined by their SEDs and their morphologies, can be quantified. At redshift z~1, the GSMF is only slightly dependent on environment, but at lower redshifts the shapes of the GSMFs in high- and low-density environments become extremely different, with high density regions exhibiting a marked bimodality. As a result, we infer that galaxy evolution depends on both the stellar mass and the environment, the latter setting the probability of a galaxy to have a given mass: all the galaxy properties related to the stellar mass show a dependence on environment, reflecting the difference observed in the mass functions. The shapes of the GSMFs of early- and late-type galaxies are almost identical for the extremes of the density contrast we consider. The evolution toward z=0 of the mass at which the early- and late-type GSMFs match each other is more rapid in high density environments. The comparison of the observed GSMFs to the same quantities derived from a set of mock catalogues shows that blue galaxies in sparse environments are overproduced in the semi-analytical models at intermediate and high masses, because of a deficit of star formation suppression, while at z<0.5 an excess of red galaxies is present in dense environments at intermediate and low masses, because of the overquenching of satellites. ABRIDGED
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