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We study the effects of local environment and stellar mass on galaxyproperties using a mass complete sample of quiescent and star-forming systemsin the COSMOS field at $z\lesssim$ 3. We show that at $z\lesssim$ 1, the medianstar-formation rate (SFR) and specific SFR (sSFR) of all galaxies depend onenvironment, but they become independent of environment at $z\gtrsim$ 1.However, we find that only for \textit{star-forming} galaxies, the median SFRand sSFR are similar in different environments, regardless of redshift andstellar mass. We find that the quiescent fraction depends on environment at$z\lesssim$ 1, and on stellar mass out to $z\sim$ 3. We show that at$z\lesssim$ 1, galaxies become quiescent faster in denser environments and thatthe overall environmental quenching efficiency increases with cosmic time.Environmental and mass quenching processes depend on each other. At $z\lesssim$1, denser environments more efficiently quench galaxies with higher masses(log($M/M_{\odot}$)$\gtrsim$ 10.7), possibly due to a higher merger rate ofmassive galaxies in denser environments, and that mass quenching is moreefficient in denser regions. We show that the overall mass quenching efficiency($\epsilon_{mass}$) for more massive galaxies (log($M/M_{\odot}$)$\gtrsim$10.2) rises with cosmic time until $z\sim$ 1 and flattens out since then.However, for less massive galaxies, the rise in $\epsilon_{mass}$ continues tothe present time. Our results suggest that environmental quenching is onlyrelevant at $z\lesssim$ 1, likely a fast process, whereas mass quenching is thedominant mechanism at $z\gtrsim$ 1, with a possible stellar feedback physics.

Effects of Local Environment and Stellar Mass on Galaxy Quenching out to z~3