  Rocky planets in compact configurations are the most common ones around M
dwarfs. Many disks around very low mass stars (between 0.1 and 0.5 M$_\odot$)
are rather compact and small (without observable substructures and radius less
than 20 au), which favours the idea of an efficient radial drift that could
enhance planet formation in compact orbits. We aim to investigate the potential
formation paths of the observed close-in rocky exoplanet population around M
dwarfs, assuming that planet formation could take place in compact disks with
an efficient dust radial drift. We developed N-body simulations that include a
sample of embryos growing by pebble accretion exposed to planet-disk
interactions, star-planet tidal interactions and general relativistic
corrections. For a star of 0.1 M$_\odot$ we considered different gas disk
viscosity and initial embryo distributions. We also explore planet formation by
pebble accretion around stars of 0.3 and 0.5 M$_\odot$. Lastly, for each
stellar mass, we run simulations that include a sample of embryos growing by
planetesimal accretion. Our main result is that the sample of simulated planets
that grow by pebble accretion in a gas disk with low viscosity
($\alpha=10^{-4}$) can reproduce the close-in low-mass exoplanet population
around M dwarfs in terms of multiplicity, masses and semi-major axis.
Furthermore, we found that a gas disk with high viscosity ($\alpha=10^{-3}$)
can not reproduce the observed planet masses. Also, we show that planetesimal
accretion favours the formation of smaller planets than the ones formed by
pebble accretion. Rocky planet formation around M dwarfs can take place in
compact and small dust disks driven by an efficient radial drift in a gas disk
with low viscosity. This result points towards a new approach in the direction
of the disk conditions needed for rocky planet formation around very low mass
stars.
