  This is a report of a talk given at the Oberwolfach workshop on "cohomology
of finite groups: Interactions and applications" which was held during July
25th - July 31st, 2010. It is an announcement of some of the results (with
motivation) and their applications from the paper "Quotients of absolute Galois
groups which determine the entire Galois cohomology"; see arXiv:0905.1364.
