We present the first photometric redshift distribution for a large sample of 870 \mu m SMGs with robust identifications based on observations with ALMA .
In our analysis we consider 96 SMGs in the ECDFS , 77 of which have 4–19 band photometry .
We model the SEDs for these 77 SMGs , deriving a median photometric redshift of z _ { phot } = 2.3 \pm 0.1 .
The remaining 19 SMGs have insufficient photometry to derive photometric redshifts , but a stacking analysis of Herschel observations confirms they are not spurious .
Assuming that these SMGs have an absolute H –band magnitude distribution comparable to that of a complete sample of z \sim 1–2 SMGs , we demonstrate that they lie at slightly higher redshifts , raising the median redshift for SMGs to z _ { phot } = 2.5 \pm 0.2 .
Critically we show that the proportion of galaxies undergoing an SMG-like phase at z \geq 3 is at most 35 \pm 5 per cent of the total population .
We derive a median stellar mass of M _ { \star } = ( 8 \pm 1 ) \times 10 ^ { 10 } M _ { \odot } , although there are systematic uncertainties of up to 5 \times for individual sources .
Assuming that the star formation activity in SMGs has a timescale of \sim 100 Myr we show that their descendants at z \sim 0 would have a space density and M _ { H } distribution which are in good agreement with those of local ellipticals .
In addition the inferred mass-weighted ages of the local ellipticals broadly agree with the look-back times of the SMG events .
Taken together , these results are consistent with a simple model that identifies SMGs as events which form most of the stars seen in the majority of luminous elliptical galaxies at the present day .