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[Abridged] We use the final data of the VIMOS Public Extragalactic RedshiftSurvey (VIPERS) to investigate the effect of environment on the evolution ofgalaxies between $z=0.5$ and $z=0.9$. We characterise local environment interms of the density contrast smoothed over a cylindrical kernel, the scale ofwhich is defined by the distance to the $5^{th}$ nearest neighbour. We findthat more massive galaxies tend to reside in higher-density environments overthe full redshift range explored. Defining star-forming and passive galaxiesthrough their (NUV$-r$) vs ($r-K$) colours, we then quantify the fraction ofstar-forming over passive galaxies, $f_{\rm ap}$, as a function of environmentat fixed stellar mass. $f_{\rm ap}$ is higher in low-density regions forgalaxies with masses ranging from $\log(\mathcal{M}/\mathcal{M}_\odot)=10.38$(the lowest value explored) to at least$\log(\mathcal{M}/\mathcal{M}_\odot)\sim11.3$, although with decreasingsignificance going from lower to higher masses. This is the first time thatenvironmental effects on high-mass galaxies are clearly detected at redshiftsas high as $z\sim0.9$. We compared these results to VIPERS-like galaxy mockcatalogues based on the galaxy formation model of De Lucia & Blaizot. The modelcorrectly reproduces $f_{\rm ap}$ in low-density environments, butunderpredicts it at high densities. The discrepancy is particularly strong forthe lowest-mass bins. We find that this discrepancy is driven by an excess oflow-mass passive satellite galaxies in the model. Looking at the accretionhistory of these model galaxies, i.e. the times when they become satellites, abetter (yet not perfect) agreement with observations can be obtained in highdensity regions by assuming either that a not-negligible fraction of satellitesis destroyed, or that their quenching time-scale is longer than $\sim 2$ Gyr.

The VIMOS Public Extragalactic Redshift Survey (VIPERS). The decline of cosmic star formation: quenching, mass, and environment connections