  We investigate the evolution of the star formation rate (SFR)-density
relation in the Extended Chandra Deep Field South (ECDFS) and the Great
Observatories Origin Deep Survey (GOODS) fields up to z~1.6. In addition to the
"traditional method", in which the environment is defined according to a
statistical measurement of the local galaxy density, we use a "dynamical"
approach, where galaxies are classified according to three different
environment regimes: group, "filament-like", and field. Both methods show no
evidence of a SFR-density reversal. Moreover, group galaxies show a mean SFR
lower than other environments up to z~1, while at earlier epochs group and
field galaxies exhibit consistent levels of star formation (SF) activity. We
find that processes related to a massive dark matter halo must be dominant in
the suppression of the SF below z~1, with respect to purely density-related
processes. We confirm this finding by studying the distribution of galaxies in
different environments with respect to the so-called Main Sequence (MS) of
star-forming galaxies. Galaxies in both group and "filament-like" environments
preferentially lie below the MS up to z~1, with group galaxies exhibiting lower
levels of star-forming activity at a given mass. At z>1, the star-forming
galaxies in groups reside on the MS. Groups exhibit the highest fraction of
quiescent galaxies up to z~1, after which group, "filament-like", and field
environments have a similar mix of galaxy types. We conclude that groups are
the most efficient locus for star-formation quenching. Thus, a fundamental
difference exists between bound and unbound objects, or between dark matter
haloes of different masses.
