  We investigate the cross-correlation between the spatial distribution of
Lyman Break Galaxies (LBGs) and the 21cm intensity mapping signal at
$z\sim[3-5]$. At these redshifts, galactic feedback is supposed to only
marginally affect the matter power spectrum, and the neutral hydrogen
distribution is independently constrained by quasar spectra. Using a high
resolution N-body simulation, populated with neutral hydrogen a posteriori, we
forecast for the expected LBG-21cm cross-spectrum and its error for a 21cm
field observed by the Square Kilometre Array (SKA1-LOW and SKA1-MID), combined
with a spectroscopic LBG survey with the same volume. The cross power can be
detected with a signal-to-noise ratio (SNR) up to ~10 times higher (and down to
~4 times smaller scales) than the 21cm auto-spectrum for this set-up, with the
SNR depending only very weakly on redshift and the LBG population. We also show
that while both the 21cm auto- and LBG-21cm cross-spectra can be reliably
recovered after the cleaning of smooth-spectrum foreground contamination, only
the cross-power is robust to problematic non-smooth foregrounds like polarized
synchrotron emission.
