  We present ALMA observations of the 870$\mu$m continuum and CO(4-3) line
emission in the core of the galaxy cluster ClJ1449+0856 at z=2, a NIR-selected,
X-ray detected system in the mass range of typical progenitors of today's
massive clusters. The 870$\mu$m map reveals six F$_{870\mu m}$ > 0.5 mJy
sources spread over an area of 0.07 arcmin$^2$, giving an overdensity of a
factor ~10 (6) with respect to blank field counts down to F$_{870\mu m}$ > 1
(0.5) mJy. On the other hand, deep CO(4-3) follow-up confirms membership of
three of these sources, but suggests that the remaining three, including the
brightest 870$\mu$m sources in the field (F$_{870\mu m}\gtrsim$2 mJy), are
likely interlopers. The measurement of 870$\mu$m continuum and CO(4-3) line
fluxes at the positions of previously-known cluster members provides a deep
probe of dusty star formation occurring in the core of this high-redshift
structure, adding up to a total SFR~700$\pm$100 M$_{\odot}$/yr and yielding an
integrated star formation rate density of ~10$^4$ M$_{\odot}$/yr/Mpc$^3$, five
orders of magnitude larger than in the field at the same epoch, due to the
concentration of star-forming galaxies in the small volume of the dense cluster
core. The combination of these observations with previously available HST
imaging highlights the presence in this same volume of a population of galaxies
with already suppressed star formation. This diverse composition of galaxy
populations in ClJ1449+0856 is especially highlighted at the very cluster
center, where a complex assembly of quiescent and star-forming sources is
likely forming the future Brightest Cluster Galaxy.
