  We analyzed 3 years of data from the Kepler space mission to derive rotation
periods of main-sequence stars below 6500 K. Our automated
autocorrelation-based method detected rotation periods between 0.2 and 70 days
for 34,030 (25.6%) of the 133,030 main-sequence Kepler targets (excluding known
eclipsing binaries and Kepler Objects of Interest), making this the largest
sample of stellar rotation periods to date. In this paper we consider the
detailed features of the now well-populated period-temperature distribution and
demonstrate that the period bimodality, first seen by McQuillan, Aigrain &
Mazeh (2013) in the M-dwarf sample, persists to higher masses, becoming less
visible above 0.6 M_sun. We show that these results are globally consistent
with the existing ground-based rotation-period data and find that the upper
envelope of the period distribution is broadly consistent with a
gyrochronological age of 4.5 Gyrs, based on the isochrones of Barnes (2007),
Mamajek & Hillenbrand (2008) and Meibom et al. (2009). We also performed a
detailed comparison of our results to those of Reinhold et al. (2013) and
Nielsen et al. (2013), who have measured rotation periods of field stars
observed by Kepler. We examined the amplitude of periodic variability for the
stars with detected rotation periods, and found a typical range between ~950
ppm (5th percentile) and ~22,700 ppm (95th percentile), with a median of ~5,600
ppm. We found typically higher amplitudes for shorter periods and lower
effective temperatures, with an excess of low-amplitude stars above ~5400 K.
