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We investigate the properties of a sample of 35 galaxies, detected with ALMAat 1.1 mm in the GOODS-ALMA field (area of 69 arcmin$^2$, resolution = 0.60",RMS $\simeq$ 0.18 mJy beam$^{-1}$). Using the UV-to-radio deep multiwavelengthcoverage of the GOODS-South field, we fit the spectral energy distributions ofthese galaxies to derive their key physical properties. The galaxies detectedby ALMA are among the most massive at $z$ = 2-4 (M$_{\star,med}$ = 8.5$ \times$10$^{10}$ M$_\odot$) and are either starburst or located in the upper part ofthe galaxy star-forming main sequence. A significant portion of our galaxypopulation ($\sim$ 40%), located at $z\sim$ 2.5-3, exhibits abnormally low gasfractions. The sizes of these galaxies, measured with ALMA, are compatible withthe trend between $H$-band size and stellar mass observed for $z\sim2$elliptical galaxies suggesting that they are building compact bulges. We showthat there is a strong link between star formation surface density (at 1.1 mm)and gas depletion time: the more compact a galaxy's star-forming region is, theshorter its lifetime will be (without gas replenishment). The identifiedcompact sources associated with relatively short depletion timescales($\sim$100 Myr), are the ideal candidates to be the progenitors of compactelliptical galaxies at $z$ $\sim$ 2.

GOODS-ALMA: The slow downfall of star-formation in $z$ = 2-3 massive galaxies