La formule des traces pour les rev\^etements de groupes r\'eductifs connexes. III. Le d\'eveloppement spectral fin

We pursue Arthur's invariant trace formula for certain coverings of connected reductive groups by deducing explicit formulas for its spectral side. This is based on some results in local harmonic analysis from an earlier preprint. The arguments are due to Arthur, and we will explain the necessary fine-tunings for coverings.