Despite targets of many multiwavelength campaigns, the main physical processes at work in AGN are still under debate. In particular the origin of the radio emission and the mechanisms involved are among the open questions in astrophysics. In the radio-loud AGN population the radio emission is linked to the presence of bipolar outflows of relativistic jets. However, the large majority of the AGN population do not form powerful highly-relativistic jets on kpc scales and are characterized by radio luminosity up to 10^23 W/Hz at 1.4 GHz, challenging our knowledge on the physical processes at the basis of the radio emission in radio-quiet objects. The main mechanisms proposed so far are synchrotron radiation from mildly relativistic mini-jets, thermal cyclo-synchrotron emission by low-efficiency accretion flow (like ADAF or ADIOS), or thermal free-free emission from the X-ray heated corona or wind. The difficulty in understanding the main mechanism involved is related to the weakness of these objects, which precludes the study of non-local radio-quiet AGN. Multifrequency, high-sensitivity radio observations are crucial to constrain the nature of the power engine, and they may help in distinguishing between the contribution from star formation and AGN activity. The advent of the SKA, with its sub-arcsecond resolution and unprecedented sensitivity will allow us to investigate these processes in radio-quiet AGN, even at high redshift for the first time. Both the broad-band radio spectrum and the polarization information will help us in disentangling between non-thermal and thermal origin of the radio emission. The jump in sensitivity of a few order of magnitudes at the (sub-)uJy level will enable us to detect radio emission from a large number of radio-quiet AGN at high redshift, providing a fundamental step in our understanding of their cosmological evolution. (Abridged)
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