  We present the Galaxy Stellar Mass Function (MF) up to z~1 from the
zCOSMOS-bright 10k spectroscopic sample. We investigate the total MF and the
contribution of ETGs and LTGs, defined by different criteria (SED, morphology
or star formation). We unveil a galaxy bimodality in the global MF, better
represented by 2 Schechter functions dominated by ETGs and LTGs, respectively.
For the global population we confirm that low-mass galaxies number density
increases later and faster than for massive galaxies. We find that the MF
evolution at intermediate-low values of Mstar (logM<10.6) is mostly explained
by the growth in stellar mass driven by smoothly decreasing star formation
activities. The low residual evolution is consistent with ~0.16 merger per
galaxy per Gyr (of which fewer than 0.1 are major). We find that ETGs increase
in number density with cosmic time faster for decreasing Mstar, with a median
"building redshift" increasing with mass, in contrast with hierarchical models.
For LTGs we find that the number density of blue or spiral galaxies remains
almost constant from z~1. Instead, the most extreme population of active star
forming galaxies is rapidly decreasing in number density. We suggest a
transformation from blue active spirals of intermediate mass into blue
quiescent and successively (1-2 Gyr after) into red passive types. The complete
morphological transformation into red spheroidals, required longer time-scales
or follows after 1-2 Gyr. A continuous replacement of blue galaxies is expected
by low-mass active spirals growing in stellar mass. We estimate that on average
~25% of blue galaxies is transforming into red per Gyr for logM<11. We conclude
that the build-up of galaxies and ETGs follows the same downsizing trend with
mass as the formation of their stars, converse to the trend predicted by
current SAMs. We expect a negligible evolution of the global Galaxy Baryonic
MF.
