(Proposal ID) S13B-018 (PI) Kashikawa, Nobunari (Proposal Title) Spectroscopy for a Very Faint High-z quasar at z~6 (Abstract) We propose to take follow-up 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 identified two z~6 quasars with Lyalpha emissions out of 15 quasar candidates. Their zR magnitudes gives M_1450 ~ -23.5, which is much fainter than the previous sample. We would like to certainly identify Mg ii using IRCS-LGS for one of our targtes, which is observable at semester S13B. Our immediate objective of this observation is to estimate BH mass and Eddington ratio for the least massive BH at z~6 from measuring 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 with high-sensitivity power of LGS. Even only one measurement provides us a precious opportunity to investigate the growing phase of SMBH in early universe. This observation targeting for a faint quasar will also give a unique independent verification of the faint end slope of QLF at z~6, in which several BH evolution models make qualitatively different predictions.