Dwarf galaxies are thought to host the remnants of the early Universe seed black holes (BHs) and to be dominated by supernova feedback. However, recent studies suggest that BH feedback could also strongly impact their growth. We report the discovery of 35 dwarf galaxies hosting radio AGN out to redshift $sim$3.4, which constitutes the highest-redshift sample of AGN in dwarf galaxies. The galaxies are drawn from the VLA-COSMOS 3 GHz Large Project and all are star-forming. After removing the contribution from star formation to the radio emission, we find a range of AGN radio luminosities of $L^mathrm{AGN}_mathrm{1.4 GHz} sim 10^{37}$-$10^{40}$ erg s$^{-1}$. The bolometric luminosities derived from the fit of their spectral energy distribution are $gtrsim 10^{42}$ erg s$^{-1}$, in agreement with the presence of AGN in these dwarf galaxies. The 3 GHz radio emission of most of the sources is compact and the jet powers range from $Q_mathrm{jet} sim 10^{42}$ to 10$^{44}$ erg s$^{-1}$. These values, as well as the finding of jet efficiencies $geq 10$ % in more than 50% of the sample, indicate that dwarf galaxies can host radio jets as powerful as those of massive radio galaxies whose jet mechanical feedback can strongly affect the formation of stars in the host galaxy. We conclude that AGN feedback can also have a very strong impact on dwarf galaxies, either triggering or hampering star formation and possibly the material available for BH growth. This implies that those low-mass AGN hosted in dwarf galaxies might not be the untouched relics of the early seed BHs, which has important implications for seed BH formation models.
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