(Proposal ID) S13A-046 (PI) Kashikawa Nobunari (Proposal Title) Spectroscopy for a Very Faint High-z quasar at z~6 (Abstract) We propose to take deep optical/NIR spectroscopy for our promising faint quasar candidate at z=6. We have searched quasar candidates at z~6 and 7 with Suprime-Cam for 7 deg^2 in total for three UKIDSS-DXS fields. Our preliminary follow-up spectroscopy with DEIMOS with short exposure time revealed one plausible Ly alpha emission at 8559Angstrom, which corresponds to z=6.04, out of 9 quasar candidates at z~6. Its z_R magnitudes gives M_1450=-23.23, which is much fainter than the previous sample. We would like to certainly identify its Ly alpha emission and Mg II, using FOCAS and IRCS-LGS. Our immediate objective of this observation is to confirm that it is a real faint quasar at z=6. This observation targeting for a faint quasar at M_1450=-23.23 will give a unique independent verification of the shape of QLF at z~6. It is quite important to observationally determine the faint end slope of QLF at high-z, in which several BH evolution models make qualitatively different predictions. The SMBH mass and the Eddington ratio can be evaluated from the velocity width of the Mg II emission. The current BH mass measurements at z=6 is limited by M_1450<-24.28, and this observation aims, for the first time, to overcome the limit.