Mapping Galaxy Clusters in the Distant Universe
  We present the science case for mapping several thousand galaxy
(proto)clusters at z=1-10 with a large aperture single dish sub-mm facility,
producing a high-redshift counterpart to local large surveys of rich clusters
like the well-studied Abell catalogue. Principal goals of a large survey of
distant clusters are the evolution of galaxy clusters over cosmic time and the
impact of environment on the evolution and formation of galaxies. To make a big
leap forward in this emerging research field, the community would benefit from
a large-format, wide-band, direct-detection spectrometer (e.g., based on MKID
technology), covering a wide field of ~1 square degree and a frequency coverage
from 70 to 700 GHz.
