  We present the detection of CO(5-4) with S/N> 7 - 13 and a lower CO
transition with S/N > 3 (CO(4-3) for 4 galaxies, and CO(3-2) for one) with ALMA
in band 3 and 4 in five main sequence star-forming galaxies with stellar masses
3-6x10^10 M/M_sun at 3 < z < 3.5. We find a good correlation between the total
far-infrared luminosity LFIR and the luminosity of the CO(5-4) transition
L'CO(5-4), where L'CO(5-4) increases with SFR, indicating that CO(5-4) is a
good tracer of the obscured SFR in these galaxies. The two galaxies that lie
closer to the star-forming main sequence have CO SLED slopes that are
comparable to other star-forming populations, such as local SMGs and BzK
star-forming galaxies; the three objects with higher specific star formation
rates (sSFR) have far steeper CO SLEDs, which possibly indicates a more
concentrated episode of star formation. By exploiting the CO SLED slopes to
extrapolate the luminosity of the CO(1-0) transition, and using a classical
conversion factor for main sequence galaxies of alpha_CO = 3.8 M_sun(K km s^-1
pc^-2)^-1, we find that these galaxies are very gas rich, with molecular gas
fractions between 60 and 80%, and quite long depletion times, between 0.2 and 1
Gyr. Finally, we obtain dynamical masses that are comparable with the sum of
stellar and gas mass (at least for four out of five galaxies), allowing us to
put a first constraint on the alpha_CO parameter for main sequence galaxies at
an unprecedented redshift.
