The contribution of major mergers to galaxy mass assembly along cosmic time is an important ingredient to the galaxy evolution scenario. We aim to measure the evolution of the merger rate for both luminosity/mass selected galaxy samples and investigate its dependence with the local environment. We use a sample of 10644 spectroscopically observed galaxies from the zCOSMOS redshift survey to identify pairs of galaxies destined to merge, using only pairs for which the velocity difference and projected separation of both components with a confirmed spectroscopic redshift indicate a high probability of merging. We have identified 263 spectroscopically confirmed pairs with r_p^{max} = 100 h^{-1} kpc. We find that the density of mergers depends on luminosity/mass, being higher for fainter/less massive galaxies, while the number of mergers a galaxy will experience does not depends significantly on its intrinsic luminosity but rather on its stellar mass. We find that the pair fraction and merger rate increase with local galaxy density, a property observed up to redshift z=1. We find that the dependence of the merger rate on the luminosity or mass of galaxies is already present up to redshifts z=1, and that the evolution of the volumetric merger rate of bright (massive) galaxies is relatively flat with redshift with a mean value of 3*10^{-4} (8*10^{-5} respectively) mergers h^3 Mpc^{-3} Gyr^{-1}. The dependence of the merger rate with environment indicates that dense environments favors major merger events as can be expected from the hierarchical scenario. The environment therefore has a direct impact in shapping-up the mass function and its evolution therefore plays an important role on the mass growth of galaxies along cosmic time.
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