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Recent estimates point to abundances of z > 4 sub-millimeter (sub-mm)galaxies far above model predictions. The matter is still debated. According tosome analyses the excess may be substantially lower than initially thought andperhaps accounted for by flux boosting and source blending. However, there isno general agreement on this conclusion. An excess of z > 6 dusty galaxies hasalso been reported albeit with poor statistics. On the other hand, evidence ofa top-heavy initial mass function (IMF) in high-z starburst galaxies has beenreported in the past decades. This would translate into a higher sub-mmluminosity of dusty galaxies at fixed star formation rate, i.e., into a higherabundance of bright high-z sub-mm galaxies than expected for a universalChabrier IMF. Exploiting our physical model for high-z proto-spheroidalgalaxies, we find that part of the excess can be understood in terms of an IMFsomewhat top-heavier than Chabrier. Such IMF is consistent with that recentlyproposed to account for the low 13C/18O abundance ratio in four dusty starburstgalaxies at z = 2-3. However, extreme top-heavy IMFs are inconsistent with thesub-mm counts at z > 4.

High-z dusty star-forming galaxies: a top-heavy initial mass function?