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  1. Abstract The high-frequency radio sky has historically remained largely unexplored due to the typical faintness of sources in this regime, and the modest survey speed compared to observations at lower frequencies. However, high-frequency radio surveys offer an invaluable tracer of high-redshift star formation, as they directly target the faint radio free–free emission. We present deep continuum observations at 34 GHz in the COSMOS and GOODS-North fields from the Karl G. Jansky Very Large Array (VLA), as part of the COLD z survey. The deep COSMOS mosaic spans down to σ = 1.3 μ Jy beam −1 , while the wider GOODS-N observations cover to σ = 5.3 μ Jy beam −1 . We detect a total of 18 galaxies at 34 GHz, of which nine show radio emission consistent with being powered by star formation; although for two sources, this is likely due to thermal emission from dust. Utilizing deep ancillary radio data at 1.4, 3, 5, and 10 GHz, we decompose the spectra of the remaining seven star-forming galaxies into their synchrotron and thermal free–free components, and find typical thermal fractions and synchrotron spectral indices comparable to those observed in local star-forming galaxies. We further determine free–free star formationmore »rates (SFRs), and show that these are in agreement with SFRs from spectral energy distribution-fitting and the far-infrared/radio correlation. Our observations place strong constraints on the high-frequency radio emission in typical galaxies at high redshift, and provide some of the first insights into what is set to become a key area of study with future radio facilities, such as the Square Kilometer Array Phase 1 and next-generation VLA.« less