  We study the impact of a warm dark matter (WDM) cosmology on dwarf galaxy
formation through a suite of cosmological hydrodynamical zoom-in simulations of
$M_{\rm halo} \approx10^{10}\,M_{\odot}$ dark matter halos as part of the
Feedback in Realistic Environments (FIRE) project. A main focus of this paper
is to evaluate the combined effects of dark matter physics and stellar feedback
on the well-known small-scale issues found in cold dark matter (CDM) models. We
find that the $z=0$ stellar mass of a galaxy is strongly correlated with the
central density of its host dark matter halo at the time of formation, $z_{\rm
f}$, in both CDM and WDM models. WDM halos follow the same
$M_{\star}(z=0)-V_{\rm max}(z_{\rm f})$ relation as in CDM, but they form
later, are less centrally dense, and therefore contain galaxies that are less
massive than their CDM counterparts. As a result, the impact of baryonic
effects on the central gravitational potential is typically diminished relative
to CDM. However, the combination of delayed formation in WDM and energy input
from stellar feedback results in dark matter profiles with lower overall
densities. The WDM galaxies studied here have a wider diversity of star
formation histories (SFHs) than the same systems simulated in CDM, and the two
lowest $M_{\star}$ WDM galaxies form all of their stars at late times. The
discovery of young ultra-faint dwarf galaxies with no ancient star formation --
which do not exist in our CDM simulations -- would therefore provide evidence
in support of WDM.
