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We present ALMA [CII] line and far-infrared (FIR) continuum observations ofthree $z > 6$ low-luminosity quasars ($M_{\rm 1450} > -25$) discovered by ourSubaru Hyper Suprime-Cam (HSC) survey. The [CII] line was detected in all threetargets with luminosities of $(2.4 - 9.5) \times 10^8~L_\odot$, about one orderof magnitude smaller than optically luminous ($M_{\rm 1450} \lesssim -25$)quasars. The FIR continuum luminosities range from $< 9 \times 10^{10}~L_\odot$(3$\sigma$ limit) to $\sim 2 \times 10^{12}~L_\odot$, indicating a wide rangein star formation rates in these galaxies. Most of the HSC quasars studied thusfar show [CII]/FIR luminosity ratios similar to local star-forming galaxies.Using the [CII]-based dynamical mass ($M_{\rm dyn}$) as a surrogate for bulgestellar mass ($M_{\rm bulge}$), we find that a significant fraction oflow-luminosity quasars are located on or even below the local $M_{\rm BH} -M_{\rm bulge}$ relation, particularly at the massive end of the galaxy massdistribution. In contrast, previous studies of optically luminous quasars havefound that black holes are overmassive relative to the local relation. Giventhe low luminosities of our targets, we are exploring the nature of the earlyco-evolution of supermassive black holes and their hosts in a less biased way.Almost all of the quasars presented in this work are growing their black holemass at much higher pace at $z \sim 6$ than the parallel growth model, in whichsupermassive black holes and their hosts grow simultaneously to match the local$M_{\rm BH} - M_{\rm bulge}$ relation at all redshifts. As the low-luminosityquasars appear to realize the local co-evolutionary relation even at $z \sim6$, they should have experienced vigorous starbursts prior to the currentlyobserved quasar phase to catch up with the relation.

Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs) VIII. A less biased view of the early co-evolution of black holes and host galaxies