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The 21-cm spectral line widths, $w_{50}$, of galaxies are an approximatetracer of their dynamical masses, such that the dark matter halo mass functionis imprinted in the number density of galaxies as a function of $w_{50}$.Correcting observed number counts for survey incompleteness at the level ofaccuracy needed to place competitive constraints on warm dark matter (WDM)cosmological models is very challenging, but forward-modelling the results ofcosmological hydrodynamical galaxy formation simulations into observationaldata space is more straightforward. We take this approach to make predictionsfor an ALFALFA-like survey from simulations using the EAGLE galaxy formationmodel in both cold (CDM) and WDM cosmogonies. We find that for WDM cosmogoniesmore galaxies are detected at the low-$w_{50}$ end of the 21-cm velocity widthfunction than in the CDM cosmogony, contrary to what might na\"ively beexpected from the suppression of power on small scales in such models. This isbecause low-mass galaxies form later and retain more gas in WDM cosmogonies(with EAGLE). While some shortcomings in the treatment of cold gas in the EAGLEmodel preclude placing definitive constraints on WDM scenarios, our analysisillustrates that near-future simulations with more accurate modelling of coldgas will likely make strong constraints possible, especially in conjunctionwith new 21-cm surveys such as WALLABY.

A warm dark matter cosmogony may yield more low-mass galaxy detections in 21-cm surveys than a cold dark matter one