We propose a deep spectroscopic survey of variability-selected AGNs at intermediate redshifts (0.5<z<4.5) constructed from the HSC-SSP ultra-deep survey in the COSMOS field. The variability-based AGN selection in the optical band provides a powerful means to search for low-mass SMBHs (MBH<106 M⊙) residing in low-luminosity AGNs, since lower luminosity AGNs tends to show larger variability amplitude. The importance of low-mass SMBH at intermediate redshifts extends to the realm of BH seeds growth and their intricate connection with their host galaxies. We select low-mass SMBH candidates within the low stellar mass range (109< Mstar/M⊙<1010) calculated from multi-wavelength SED fitting model that incorporates AGN and host galaxy components. Employing the scaling relation MBH/ Mstar∼0.025% argued in the local universe (e.g., Reines, E & Volonteri, M 2015, ApJ, 613, 682), this observation will determine the low-mass SMBH mass in the range (105< MBH / M⊙<106) at intermediate redshifts for the first time. The outcome of this research will provide valuable insights into the path of rapid growth from BH seeds to SMBH, as well as the relationship between SMBHs and host galaxies across cosmic time.
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