1. Introduction
2. Sample selection
2.1. The zCOSMOS-deep spectroscopic survey
2.2. The C IV-selected sample
2.3. Spectral measurements and AGN classification
2.4. Spectral properties of the AGN samples
2.5. X-ray properties of the AGN samples
3. The C IV-selected type 2 AGN sample
3.1. UV emission-line measurements
3.2. Stellar masses of the host galaxies
4. Comparison with photoionization models
4.1. Photoionization models
4.2. Micro turbulent clouds and inner radius of the NLR gas
4.3. Diagnostic diagrams
4.4. Physical properties of the nebular gas
5. Discussion
5.1. Nebular properties of narrow-line AGN at $z{=}1.5{-}3$
5.2. Evolution with redshift of the NLR metallicity
5.3. Mass-metallicity relationship in our type 2 AGN sample
6. Summary and conclusions