  We combine GALEX near-UV photometry with a volume-limited sample of local
(0.005<z<0.037) SDSS DR4 galaxies to examine the composition and the
environmental dependencies of the optical and UV-optical colour-magnitude (C-M)
diagrams. We find that ~30% of red sequence galaxies in the optical C-M diagram
show signs of ongoing star-formation from their spectra having EW(Halpha)>2A.
This contamination is greatest at faint magnitudes (Mr>-19) and in field
regions where as many as three-quarters of red sequence galaxies are
star-forming, and as such has important consequences for following the build-up
of the red sequence. We find that the NUV-r colour instead allows a much more
robust separation of passively-evolving and star-forming galaxies, which allows
the build-up of the UV-selected red sequence with redshift and environment to
be directly interpreted in terms of the assembly of stellar mass in
passively-evolving galaxies. We find that in isolated field regions the number
density of UV-optical red sequence galaxies declines rapidly at magnitudes
fainter than Mr~-19 and appears completely truncated at Mr~-18. This confirms
the findings of Haines et al. (2007) that no passively-evolving dwarf galaxies
are found more than two virial radii from a massive halo, whether that be a
group, cluster or massive galaxy. These results support the downsizing paradigm
whereby the red sequence is assembled from the top down, being already largely
in place at the bright end by z~1, and the faint end filled in at later epochs
in clusters and groups through environment-related processes such as
ram-pressure stripping or galaxy harassment.
