(Proposal ID) S15B-173 (PI) Schramm, Malte (Proposal Title) Evolution of the M_{BH}-M_{stell} relation at z~4 (Abstract) We propose IRCS+AO188 H,K-band imaging to obtain rest-frame optical luminosities, colors and morphological properties of a sample of low luminosity QSO host galaxies at redshifts z=3-4 selected from the COSMOS survey and SDSS. This study is a continuation of our observing run from S14B, which could not be completed due to bad weather conditions. We are in particular interested in completing our additional narrow-band imaging proposed in S14B to probe the extended [OIII] narrow-line region of previously observed quasars tracing the gas morphology which can only be done by AO support which provides sufficient spatial resolution to measure the properties of the QSO host galaxies beyond simple detection. All QSOs were well selected with a PSF star close to the QSO and at similar separation from the guide star. The measured colors will be converted into M/L ratios to estimate the stellar masses of the host galaxies. Our main targets are selected to have BH masses of ~10^8 M_sun (avoiding the typical selection bias), estimated from optical and NIR spectroscopy. We want to constrain the evolution of the MBH-Mbul relation, setting strong limits on the physics involved in the galaxy-BH co-evolution out to z~4.