  While it is well established that giant-planet occurrence rises rapidly with
host star metallicity, it is not yet clear if small-planet occurrence around
late-type dwarf stars depends on host star metallicity. Using the Kepler Data
Release 25 planet candidate list and its completeness data products, we explore
planet occurrence as a function of metallicity in the Kepler field's late-type
dwarf stellar population. We find that planet occurrence increases with
metallicity for all planet radii $R_{\mathrm{p}}$ down to at least
$R_{\mathrm{p}}\approx2~R_{\oplus}$ and that in the range $2~R_{\oplus}\lesssim
R_{\mathrm{p}}\lesssim 5~R_{\oplus}$ planet occurrence scales linearly with
metallicity $Z$. Extrapolating our results, we predict that short-period
planets with $R_{\mathrm{p}}\lesssim 2~R_{\oplus}$ should be rare around early
M dwarf stars with $\mathrm{[M/H]}\lesssim-0.5$ or late M dwarf stars with
$\mathrm{[M/H]}\lesssim+0.0$. This dependence of planet occurrence on
metallicity observed in the Kepler field emphasizes the need to control for
metallicity in estimates of planet occurrence for late-type dwarf stars like
those targeted by Kepler's K2 extension and the Transiting Exoplanet Survey
Satellite (TESS). We confirm the theoretical expectation that the small planet
occurrence--host star metallicity relation is stronger for low-mass stars than
for solar-type stars. We establish that the expected solid mass in planets
around late-type dwarfs in the Kepler field is comparable to the total amount
of planet-making solids in their protoplanetary disks. We argue that this high
efficiency of planet formation favors planetesimal accretion over pebble
accretion as the origin of the small planets observed by Kepler around
late-type dwarf stars.
