  Current measurements of planet population as a function of stellar mass show
three seemingly contradictory signatures: close-in super-Earths are more
prevalent around M dwarfs than FGK dwarfs; inner super-Earths are correlated
with outer giants; and outer giants are less common around M dwarfs than FGK
dwarfs. Here, we build a simple framework that combines the theory of pebble
accretion with the measurements of dust masses in protoplanetary disks to
reconcile all three observations. First, we show that cooler stars are more
efficient at converting pebbles into planetary cores at short orbital periods.
Second, when disks are massive enough to nucleate a heavy core at 5 AU, more
than enough dust can drift in to assemble inner planets, establishing the
correlation between inner planets and outer giants. Finally, while stars of
varying masses are similarly capable of converting pebbles into cores at long
orbital periods, hotter stars are much more likely to harbor more massive dust
disks so that the giant planet occurrence rate rises around hotter stars. Our
results are valid over a wide range of parameter space for a disk accretion
rate that follows $\dot{M}_\star \sim 10^{-8}\,M_\odot\,{\rm
yr}^{-1}(M_\star/M_\odot)^2$. We predict a decline in mini-Neptune population
(but not necessarily terrestrial planets) around stars lighter than $\sim
0.3-0.5 M_\odot$. Cold giants ($\gtrsim$5 AU), if they exist, should remain
correlated with inner planets even around lower mass stars.
