  Atomic monolayers represent a novel class of materials to study localized and
free excitons in two dimensions and to engineer optoelectronic devices based on
their significant optical response. Here, we investigate the role of the
substrate on the photoluminescense response of MoSe$_2$ and WSe$_2$ monolayers
exfoliated either on SiO$_2$ or epitaxially grown InGaP substrates. In the case
of MoSe$_2$, we observe a significant qualitative modification of the emission
spectrum, which is widely dominated by the trion resonance on InGaP substrates.
However, the effects of inhomogeneous broadening of the emission features are
strongly reduced. Even more strikingly, in sheets of WSe$_2$, we could
routinely observe emission lines from localized excitons with linewidths down
to the resolution limit of 70\,$\mu$ eV. This is in stark contrast to reference
samples featuring WSe$_2$ monolayers on SiO$_2$ surfaces, where the emission
spectra from localized defects are widely dominated by spectral diffusion and
blinking behaviour. Our experiment outlines the enormous potential of
III-V-monolayer hybrid architectures to obtain high quality emission signals
from atomic monolayers, which are straight forward to integrate into
nanophotonic and integrated optoelectronic devices.
