Near infrared spectroscopy and star-formation histories of 3 ≤

We present Keck–MOSFIRE H and K spectra for a sample of 24 candidate quiescent galaxies at 3 < z < 4, identified from their rest-frame UVJ colors and photometric redshifts in the ZFOURGE and 3DHST surveys. With median integration times of one hour in H and five in K, we obtain spectroscopic redshifts for half of the sample, using either Balmer absorption lines or nebular emission lines. We confirm the high accuracy of the photometric redshifts for this spectroscopically-confirmed sample, with a median |Zphot − Zspec|/(1 + Zspec) of 1.2%. Two galaxies turn out to be dusty Hα emitters at lower redshifts (z < 2.5), and these are the only two detected in the sub-mm with ALMA. High equivalent-width [O II