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We investigate the properties of massive galaxies at z=1-3.5 using HSTobservations, ground-based near-IR imaging, and Spitzer Space Telescopeobservations at 3-24 micron. We identify 153 distant red galaxies (DRGs) withJ-K > 2.3 mag (Vega) in the southern GOODS field. This sample is approximatelycomplete in stellar mass for passively evolving galaxies above 10^11 solarmasses and z < 3. The galaxies identified by this selection are roughly splitbetween objects whose optical and near-IR rest-frame light is dominated byevolved stars combined with ongoing star formation, and galaxies whose light isdominated by heavily reddened starbursts. Very few of the galaxies (< 10%) haveno indication of current star formation. Using SFR estimates that include thereradiated IR emission, the DRGs at z=1.5-3 with stellar masses > 10^11 solarmasses have specific SFRs (SFRs per unit stellar mass) ranging from 0.2 to 10Gyr^-1, with a mean value of ~2.4 Gyr^-1. The DRGs with stellar masses > 10^11solar masses and 1.5 < z < 3 have integrated specific SFRs greater the globalvalue over all galaxies. In contrast, we find that galaxies at z = 0.3-0.75with these stellar masses have integrated specific SFRs less than the globalvalue, and more than an order of magnitude lower than that for massive DRGs atz = 1.5-3. At z < 1, lower-mass galaxies dominate the overall cosmic massassembly. This suggests that the bulk of star formation in massive galaxiesoccurs at early cosmic epochs and is largely complete by z~1.5. [Abridged]Comment: Accepted for publication in the Astrophysical Journal. 25 pages, 14  figure

SpitzerObservations of Massive, Red Galaxies at High Redshift