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ALMA Cycle 2 observations of the long wavelength dust emission in 145star-forming galaxies are used to probe the evolution of star-forming ISM. Wealso develop the physical basis and empirical calibration (with 72 low-z and z~ 2 galaxies) for using the dust continuum as a quantitative probe ofinterstellar medium (ISM) masses. The galaxies with highest star formationrates (SFRs) at <z> = 2.2 and 4.4 have gas masses up to 100 times that of theMilky Way and gas mass fractions reaching 50 to 80%, i.e. gas masses 1 - 4times their stellar masses. We find a single high-z star formation law: SFR =35 M_ mol^0.89 x (1+z)_{z=2}^0.95 x (sSFR)_{MS}^0.23 \msun yr^-1 -- anapproximately linear dependence on the ISM mass and an increased star formationefficiency per unit gas mass at higher redshift. Galaxies above the MainSequence (MS) have larger gas masses but are converting their ISM into stars ona timescale only slightly shorter than those on the MS -- thus these'starbursts' are largely the result of having greatly increased gas massesrather than and increased efficiency for converting gas to stars. At z $> 1$,the entire population of star-forming galaxies has $\sim$ 2 - 5 times shortergas depletion times than low-z galaxies. These shorter depletion times indicatea different mode of star formation in the early universe -- most likelydynamically driven by compressive, high-dispersion gas motions -- a naturalconsequence of the high gas accretion rates.

ISM masses and the star formation law at Z = 1 to 6 // ALMA observations of dust continuum in 145 galaxies in the COSMOS survey field