AzTEC Half Square Degree Survey of the SHADES Fields -- I. Maps,
  Catalogues, and Source Counts
  We present the first results from the largest deep extragalactic
millimetre-wavelength survey undertaken to date. These results are derived from
maps covering over 0.7 deg^2, made at 1.1mm, using the AzTEC continuum camera
mounted on the James Clerk Maxwell Telescope. The maps were made in the two
fields originally targeted at 0.85mm with SCUBA in the SHADES project, namely
the Lockman Hole East (mapped to a depth of 0.9-1.3 mJy rms) and the Subaru XMM
Deep Field (1.0-1.7 mJy rms). The wealth of existing and forthcoming deep
multi-frequency data in these two fields will allow the bright mm source
population revealed by these images to be explored in detail in subsequent
papers. Here we present the maps themselves, a catalogue of 114
high-significance sub-millimetre galaxy detections, and a thorough statistical
analysis leading to the most robust determination to date of the 1.1mm source
number counts. Through careful comparison, we find that both the COSMOS and
GOODS North fields, also imaged with AzTEC, contain an excess of mm sources
over the new 1.1mm source-count baseline established here. In particular, our
new AzTEC/SHADES results indicate that very luminous high-redshift dust
enshrouded starbursts (S_{1.1} > 3 mJy) are 25-50% less common than would have
been inferred from these smaller surveys, thus highlighting the potential roles
of cosmic variance and clustering in such measurements. We compare number count
predictions from recent models of the evolving mm/sub-mm source population to
these SMG surveys, which provide important constraints for the ongoing
refinement of semi-analytic and hydrodynamical models of galaxy formation, and
find that all recent models over-predict the number of bright sub-millimetre
galaxies found in this survey.
