  We introduce an ALMA band 3 spectroscopic survey, targeting the brightest
submillimeter galaxies (SMGs) in the COSMOS field. Here we present the first
results based on the 18 primary SMGs that have 870 $\mu$m flux densities of
$S_{870}=12.4-19.3$ mJy and are drawn from a parent sample of 260 ALMA-detected
SMGs from the AS2COSMOS survey. We detect emission lines in 17 and determine
their redshifts to be in the range of $z=2-5$ with a median of ${3.3\pm0.3}$.
We confirm that SMGs with brighter $S_{870}$ are located at higher redshifts.
The data additionally cover five fainter companion SMGs, and we obtain line
detection in one. Together with previous studies, our results indicate that for
SMGs that satisfy our selection, their brightest companion SMGs are physically
associated with their corresponding primary SMGs in $\ge40$% of the time,
suggesting that mergers play a role in the triggering of star formation. By
modeling the foreground gravitational fields, $<10$% of the primary SMGs can be
strongly lensed with a magnification $\mu>2$. We determine that about 90\% of
the primary SMGs have lines that are better described by double Gaussian
profiles, and the median separation of the two Gaussian peaks is 430$\pm$40 km
s$^{-1}$. This allows estimates of an average baryon mass, which together with
the line dispersion measurements puts our primary SMGs on the similar
mass-$\sigma$ correlation found on local early-type galaxies. Finally, the
number density of our $z>4$ primary SMGs is found to be
$1^{+0.9}_{-0.6}\times10^6$ cMpc$^{-3}$, suggesting that they can be the
progenitors of $z\sim3-4$ massive quiescent galaxies.
