  We present host stellar velocity dispersion measurements for a sample of 88
broad-line quasars at 0.1<z<1 (46 at z>0.6) from the Sloan Digital Sky Survey
Reverberation Mapping (SDSS-RM) project. High signal-to-noise ratio coadded
spectra (average S/N~30 per 69 km/s pixel) from SDSS-RM allowed decomposition
of the host and quasar spectra, and measurement of the host stellar velocity
dispersions and black hole (BH) masses using the single-epoch (SE) virial
method. The large sample size and dynamic range in luminosity
(L5100=10^(43.2-44.7) erg/s) lead to the first clear detection of a correlation
between SE virial BH mass and host stellar velocity dispersion far beyond the
local universe. However, the observed correlation is significantly flatter than
the local relation, suggesting that there are selection biases in high-z
luminosity-threshold quasar samples for such studies. Our uniform sample and
analysis enable an investigation of the redshift evolution of the M-sigma
relation free of caveats by comparing different samples/analyses at disjoint
redshifts. We do not observe evolution of the M-sigma relation in our sample,
up to z~1, but there is an indication that the relation flattens towards higher
redshifts. Coupled with the increasing threshold luminosity with redshift in
our sample, this again suggests certain selection biases are at work, and
simple simulations demonstrate that a constant M-sigma relation is favored to
z~1. Our results highlight the scientific potential of deep coadded
spectroscopy from quasar monitoring programs, and offer a new path to probe the
co-evolution of BHs and galaxies at earlier times.
