  The galaxy population at z~6 has been the subject of intense study in recent
years, culminating in the Hubble Ultra Deep Field (HUDF) -- the deepest imaging
survey yet. A large number of high redshift galaxy candidates have been
identified within the HUDF, but until now analysis of their properties has been
hampered by the difficulty of obtaining spectroscopic redshifts for these faint
galaxies. Our ''Gemini Lyman-Alpha at Reionisation Era'' (GLARE) project has
been designed to undertake spectroscopic follow up of faint (z'<28.5) i'-drop
galaxies at z~6 in the HUDF. In a previous paper we presented preliminary
results from the first 7.5 hours of data from GLARE. In this paper we detail
the complete survey. We have now obtained 36 hours of spectroscopy on a single
GMOS slitmask from Gemini-South, with a spectral resolution of
lambda/Delta(lambda) ~ 1000. We identify five strong Lyman-alpha emitters at
z>5.5, and a further nine possible line emitters with detections at lower
significance. We also place tight constraints on the equivalent width of
Lyman-alpha emission for a further ten i'-drop galaxies and examine the
equivalent width distribution of this faint spectroscopic sample of z~6
galaxies. We find that the fraction of galaxies with little or no emission is
similar to that at z~3, but that the z~6 population has a tail of sources with
high rest frame equivalent widths. Possible explanations for this effect
include a tendency towards stronger line emission in faint sources, which may
arise from extreme youth or low metallicity in the Lyman-break population at
high redshift, or possibly a top-heavy initial mass function.
