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A strong effort has been devoted to understand the physical origin of radioemission from low-luminosity AGN (LLAGN), but a comprehensive picture is stillmissing. We used high-resolution ($\le$1 arcsec), multi-frequency (1.5, 5.5, 9and 14 GHz) NSF's Karl G. Jansky Very Large Array (VLA) observations tocharacterise the state of the nuclear region of ten Seyfert nuclei, which arethe faintest members of a complete, distance-limited sample of 28 sources. Withthe sensitivity and resolution guaranteed by the VLA-A configuration, wemeasured radio emission for six sources (NGC3185, NGC3941, NGC4477, NGC4639,NGC4698 and NGC4725), while for the remaining four (NGC0676, NGC1058, NGC2685and NGC3486) we put upper limits at tens uJy/beam level, below the previous0.12 mJy/beam level of Ho&Ulvestad (2001), corresponding to luminosities downto L$\le10^{19}$ W/Hz at 1.5 GHz for the highest RMS observation. Two sources,NGC4639 and NGC4698, exhibit spectral slopes compatible with inverted spectra($\alpha\le$0, $S_{\nu}\,\propto\,{\nu}^{-\alpha}$), hint for radio emissionfrom an optically-thick core, while NGC4477 exhibits a steep (+0.52$\pm$0.09)slope. The detected sources are mainly compact on scales $\le$ arcseconds,predominantly unresolved, except NGC3185 and NGC3941, in which the resolvedradio emission could be associated to star-formation processes. A significantX-ray - radio luminosities correlation is extended down to very lowluminosities, with slope consistent with inefficient accretion, expected atsuch low Eddington ratios. Such sources will be one of the dominant SquareKilometre Array (SKA) population, allowing a deeper understanding of thephysics underlying such faint AGN.

From radio-quiet to radio-silent: low luminosity Seyfert radio cores