  Warm Dark Matter (WDM) cosmologies are a viable alternative to the Cold Dark
Matter (CDM) scenario. Unfortunately, an accurate scrutiny of the WDM
predictions with N-body simulations has proven difficult due to numerical
artefacts. Here, we report on cosmological simulations that, for the first
time, are devoid of those problems, and thus, are able to accurately resolve
the WDM halo mass function well below the cut-off. We discover a complex
picture, with perturbations at different evolutionary stages populating
different ranges in the halo mass function. On the smallest mass scales we can
resolve, identified objects are typically centres of filaments that are
starting to collapse. On intermediate mass scales, objects typically correspond
to fluctuations that have collapsed and are in the process of relaxation,
whereas the high mass end is dominated by objects similar to haloes identified
in CDM simulations. We then explicitly show how the formation of low-mass
haloes is suppressed, which translates into a strong cut-off in the halo mass
function. This disfavours some analytic formulations that predict a halo mass
function that would extend well below the free streaming mass. We argue for a
more detailed exploration of the formation of the smallest structures expected
to form in a given cosmology, which, we foresee, will advance our overall
understanding of structure formation.
