  (abridged) We present a new near-infrared survey covering the 2 deg sq COSMOS
field. Combining our survey with Subaru B and z images we construct a deep,
wide-field optical-infrared catalogue. At Ks<23 (AB magnitudes) our survey
completeness is greater than 90% and 70% for stars and galaxies respectively
and contains 143,466 galaxies and 13,254 stars. At z~2 our catalogues contain
3931 quiescent and 25,757 star-forming BzK-selected galaxies representing the
largest and most secure sample of these objects to date. Our counts of
quiescent galaxies turns over at Ks~22 an effect which we demonstrate cannot be
due to sample incompleteness. In our survey both the number of faint and bright
quiescent objects exceeds the predictions of a semi-analytic galaxy formation
model, indicating potentially the need for further refinements in the amount of
merging and AGN feedback at z~2 in these models. We measure the angular
correlation function for each sample and find that at small scales the
correlation function for passive BzK galaxies exceeds the clustering of dark
matter. We use 30-band photometric redshifts to derive the spatial correlation
length and the redshift distributions for each object class. At Ks<22 we find
r_0^{\gamma/1.8}=7.0 +/-0.5h^{-1} Mpc for the passive BzK candidates and
4.7+/-0.8h^{-1} Mpc for the star-forming BzK galaxies. Our pBzK galaxies have
an average photometric redshift of z_p~1.4, in approximate agreement with the
limited spectroscopic information currently available. The stacked Ks image
will be made publicly available from IRSA.
