  We present an analysis of star-formation and nuclear activity in galaxies as
a function of both luminosity and environment in the SDSS DR4 dataset. Using a
sample of 27753 galaxies at 0.005<z<0.037 that is >90% complete to Mr=-18.0 we
find that the EW(Ha) distribution is strongly bimodal, allowing galaxies to be
robustly separated into passive and star-forming populations about a value
EW(Ha)=2A. In high-density regions ~70% of galaxies are passive independent of
luminosity. In the rarefied field however, the fraction of passively-evolving
galaxies is a strong function of luminosity, dropping from ~50% for Mr<-21 to
zero by Mr~-18. Indeed for the lowest luminosity range covered (-18<Mr<-16)
none of the ~600 galaxies in the lowest density quartile are passive. The few
passively-evolving dwarf galaxies in field regions appear as satellites to
bright (~L*) galaxies. The fraction of galaxies with optical AGN signatures
decreases steadily from ~50% at Mr~-21 to ~0% by Mr~-18 closely mirroring the
luminosity-dependence of the passive galaxy fraction in low-density
environments. This result reflects the increasing importance of AGN feedback
with galaxy mass for their evolution, such that the star-formation histories of
massive galaxies are primarily determined by their past merger history. In
contrast, the complete absence of passively-evolving dwarf galaxies more than
~2 virial radii from the nearest massive halo (i.e. cluster, group or massive
galaxy) indicates that internal processes, such as merging, AGN feedback or gas
consumption through star-formation, are not responsible for terminating
star-formation in dwarf galaxies. Instead the evolution of dwarf galaxies is
primarily driven by the mass of their host halo, probably through the combined
effects of tidal forces and ram-pressure stripping.
