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While most of the known debris discs present cold dust at tens of AU, a fewyoung systems exhibit hot dust analogous to the Zodiacal dust. $\eta$ Corvi isparticularly interesting as it is old and it has both, with its hot dustsignificantly exceeding the maximum luminosity of an in-situ collisionalcascade. Previous work suggested that this system could be undergoing an eventsimilar to the Late Heavy Bombardment (LHB) soon after or during a dynamicalinstability. Here we present ALMA observations of $\eta$ Corvi with aresolution of 1."2 (~22au) to study its outer belt. The continuum emission isconsistent with an axisymmetric belt, with a mean radius of 152au and radialFWHM of 46au, which is too narrow compared to models of inward scattering of anLHB-like scenario. Instead, the hot dust could be explained as material passedinwards in a rather stable planetary configuration. We also report a 4sigmadetection of CO at ~ 20au. CO could be released in situ from icy planetesimalsbeing passed in when crossing the H$_2$O or CO$_2$ ice lines. Finally, we placeconstraints on hidden planets in the disc. If a planet is sculpting the disc'sinner 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 chaoticzone on a timescale shorter than the age of the system and scatter materialinwards from the outer belt to the inner regions, thus feeding the hot dust.

ALMA observations of the $\eta$ Corvi debris disc: inward scattering of CO-rich exocomets by a chain of 3-30 M$_\oplus$ planets?