  We characterize the mass-dependent evolution in a large sample of more than
8,000 galaxies using spectroscopic redshifts drawn from the DEEP2 Galaxy
Redshift Survey in the range 0.4 < z < 1.4 and stellar masses calculated from
K-band photometry obtained at Palomar Observatory. Using restframe (U-B) color
and [OII] equivalent widths, we distinguish star-forming from passive
populations in order to explore the nature of "downsizing''--a pattern in which
the sites of active star formation shift from high mass galaxies at early times
to lower mass systems at later epochs. Over the redshift range probed, we
identify a mass limit, M_Q, above which star formation appears to be quenched.
The physical mechanisms responsible for downsizing can thus be empirically
quantified by charting the evolution in this threshold mass. We find that M_Q
decreases with time by a factor of ~3 across the redshift range sampled
according with a redshift dependence of (1+z)^3.5. To further constrain
possible quenching mechanisms, we investigate how this downsizing signal
depends on local galaxy environment. For the majority of galaxies in regions
near the median density, there is no significant correlation between downsizing
and environment. However, a trend is observed in the comparison between more
extreme environments that are more than 3 times overdense or underdense
relative to the median. Here, we find that downsizing is accelerated in
overdense regions which host higher numbers of massive, early-type galaxies and
fewer late-types as compared to the underdense regions. Our results
significantly constrain recent suggestions for the origin of downsizing and
indicate that the process for quenching star formation must, primarily, be
internally driven. (Abridged)
