The [C

Context. The [C <ns0:sc>II</ns0:sc>] fine-structure line at 157.74 μm is one of the brightest far-infrared emission lines in galaxies and an important probe of galaxy properties such as the star formation rate (SFR) and the molecular gas mass (Mmol). Aims. Using high-resolution numerical simulations, we tested the reliability of the [C <ns0:sc>II</ns0:sc>] line as a tracer of Mmol in high-redshift galaxies and investigated secondary dependences of the [C <ns0:sc>II</ns0:sc>]−Mmol relation on the SFR and metallicity. We also investigated the time evolution of the [C <ns0:sc>II</ns0:sc>] luminosity function (LF) and the relative spatial extent of [C <ns0:sc>II</ns0:sc>] emission and star formation. Methods. We post-processed galaxies from the M<ns0:sc>ARIGOLD</ns0:sc> cosmological simulations at redshifts 3 ≤ z ≤ 7 to obtain their [C <ns0:sc>II</ns0:sc>] emission. These simulations were performed with the sub-grid chemistry model, H<ns0:sc>YACINTH</ns0:sc>, to track the non-equilibrium abundances of H2, CO, C and C+ on the fly. Based on a statistical sample of galaxies at these redshifts, we investigated correlations between the [C <ns0:sc>II</ns0:sc>] line luminosity (L[C <ns0:sc>II</ns0:sc>]) and the SFR, the Mmol, the total gas mass and the metal mass in gas phase (Mmetal). Results. We find that accounting for secondary dependencies in the L[C <ns0:sc>II</ns0:sc>]−Mmol relation improves the Mmol prediction by a factor of 2.3 at all redshifts. Our simulations predict a mild evolution in the slope of the L[C <ns0:sc>II</ns0:sc>]−SFR relation (≲0.15 dex) and an increase in the intercept by 0.5 dex in the above redshift range. Among the various galaxy properties we explore, the [C <ns0:sc>II</ns0:sc>] emission in our simulated galaxies shows the tightest correlation with Mmetal, indicating the potential of this line to constrain the metallicity of high-redshift galaxies. About 20% (10%) of our simulated galaxies at z = 5 (z = 4) have [C <ns0:sc>II</ns0:sc>] emission extending ≥2 times farther than the star formation activity. The [C <ns0:sc>II</ns0:sc>] LF evolves rapidly and is always well approximated by a double power law that does not show an exponential cut-off at the bright end. We record a 600-fold increase in the number density of L[C <ns0:sc>II</ns0:sc>] ∼ 109 L⊙ emitters in 1.4 Gyr.