  While most of the known debris discs present cold dust at tens of AU, a few
young systems exhibit hot dust analogous to the Zodiacal dust. $\eta$ Corvi is
particularly interesting as it is old and it has both, with its hot dust
significantly exceeding the maximum luminosity of an in-situ collisional
cascade. Previous work suggested that this system could be undergoing an event
similar to the Late Heavy Bombardment (LHB) soon after or during a dynamical
instability. Here we present ALMA observations of $\eta$ Corvi with a
resolution of 1."2 (~22au) to study its outer belt. The continuum emission is
consistent with an axisymmetric belt, with a mean radius of 152au and radial
FWHM of 46au, which is too narrow compared to models of inward scattering of an
LHB-like scenario. Instead, the hot dust could be explained as material passed
inwards in a rather stable planetary configuration. We also report a 4sigma
detection of CO at ~ 20au. CO could be released in situ from icy planetesimals
being passed in when crossing the H$_2$O or CO$_2$ ice lines. Finally, we place
constraints on hidden planets in the disc. If a planet is sculpting the disc's
inner edge, this should be orbiting at 75-100au, with a mass of 3-30 M$_\oplus$
and an eccentricity < 0.08. Such a planet would be able to clear its chaotic
zone on a timescale shorter than the age of the system and scatter material
inwards from the outer belt to the inner regions, thus feeding the hot dust.
