  Using data from four deep fields (COSMOS, AEGIS, ECDFS, and CDFN), we study
the correlation between the position of galaxies in the star formation rate
(SFR) versus stellar mass plane and local environment at $z<1.1$. To accurately
estimate the galaxy SFR, we use the deepest available Spitzer/MIPS 24 and
Herschel/PACS datasets. We distinguish group environments (
$M_{halo}\sim$10$^{12.5-14.2}$$M_{\odot}$) based on the available deep X-ray
data and lower halo mass environments based on the local galaxy density. We
confirm that the Main Sequence (MS) of star forming galaxies is not a linear
relation and there is a flattening towards higher stellar masses (
$M_*>10^{10.4-10.6}$ $M_{\odot}$), across all environments. At high redshift (
$0.5<z<1.1$ ), the MS varies little with environment. At low redshift (
$0.15<z<0.5$ ), group galaxies tend to deviate from the mean MS towards the
region of quiescence with respect to isolated galaxies and less-dense
environments. We find that the flattening of the MS toward low SFR is due to an
increased fraction of bulge dominated galaxies at high masses. Instead, the
deviation of group galaxies from the MS at low redshift is caused by a large
fraction of red disk dominated galaxies which are not present in the lower
density environments. Our results suggest that above a mass threshold (
$\sim10^{10.4}-10^{10.6}$$M_{\odot}$ ) stellar mass, morphology and environment
act together in driving the evolution of the SF activity towards lower level.
The presence of a dominating bulge and the associated quenching processes are
already in place beyond $z\sim$1. The environmental effects appear, instead, at
lower redshifts and have a long time-scale.
