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We present a study of the radio properties of 870$\mu$m-selectedsubmillimetre galaxies (SMGs), observed at high resolution with ALMA in theExtended Chandra Deep Field South. From our initial sample of 76 ALMA SMGs, wedetect 52 SMGs at $>3\sigma$ significance in VLA 1400MHz imaging, of which 35are also detected at $>3\sigma$ in new 610MHz GMRT imaging. Within this sampleof 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 viathe parameter $q_{\rm IR}$, the logarithmic ratio of the rest-frame8-1000$\mu$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 thattypically seen in single-dish 870$\mu$m-selected sources ($q_{\rm IR} \sim2.4$), which may reflect the fact that our ALMA-based study is not biased toradio-bright counterparts, as previous samples were. Finally, we search forevidence that $q_{\rm IR}$ and $\alpha$ evolve with age in a co-dependentmanner, as predicted by starburst models: the data populate the predictedregion of parameter space, with the stellar mass tending to increase alongtracks of $q_{\rm IR}$ versus $\alpha$ in the direction expected, providing thefirst observational evidence in support of these models.

An ALMA survey of submillimetre galaxies in the Extended Chandra Deep Field South: radio properties and the far-infrared/radio correlation