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This is a report of a talk given at the Oberwolfach workshop on "cohomologyof finite groups: Interactions and applications" which was held during July25th - July 31st, 2010. It is an announcement of some of the results (withmotivation) and their applications from the paper "Quotients of absolute Galoisgroups which determine the entire Galois cohomology"; see arXiv:0905.1364.

A small quotient of the big absolute Galois group (joint work with Ido Efrat and J\'{a}n Min\'{a}\v{c})