  We present a study of the radio properties of 870$\mu$m-selected
submillimetre galaxies (SMGs), observed at high resolution with ALMA in the
Extended Chandra Deep Field South. From our initial sample of 76 ALMA SMGs, we
detect 52 SMGs at $>3\sigma$ significance in VLA 1400MHz imaging, of which 35
are also detected at $>3\sigma$ in new 610MHz GMRT imaging. Within this sample
of radio-detected SMGs, we measure a median radio spectral index
$\alpha_{610}^{1400} = -0.79 \pm 0.06$, (with inter-quartile range
$\alpha=[-1.16,-0.56]$) and investigate the far-infrared/radio correlation via
the parameter $q_{\rm IR}$, the logarithmic ratio of the rest-frame
8-1000$\mu$m flux and monochromatic radio flux. Our median $q_{\rm IR} = 2.56
\pm 0.05$ (inter-quartile range $q_{\rm IR}=[2.42,2.78]$) is higher than that
typically seen in single-dish 870$\mu$m-selected sources ($q_{\rm IR} \sim
2.4$), which may reflect the fact that our ALMA-based study is not biased to
radio-bright counterparts, as previous samples were. Finally, we search for
evidence that $q_{\rm IR}$ and $\alpha$ evolve with age in a co-dependent
manner, as predicted by starburst models: the data populate the predicted
region of parameter space, with the stellar mass tending to increase along
tracks of $q_{\rm IR}$ versus $\alpha$ in the direction expected, providing the
first observational evidence in support of these models.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics