Sunil K. Chebolu, Ido Efrat and Jan Minac: Quotients of absolute Galois groups which determine the entire Galois cohomology,,

Submission: 2009, Sep 25

For prime power q=p^d and a field F containing a root of unity of order q we show that the Galois cohomology ring H^*(G_F,Z/q) is determined by a quotient G_F^{[3]} of the absolute Galois group G_F related to its descending q-central sequence. Conversely, we show that G_F^{[3]} is determined by the lower cohomology of G_F. This is used to give new examples of pro-p groups which do not occur as absolute Galois groups of fields.

2000 Mathematics Subject Classification: 12G05, 12F10, 12E30

Keywords and Phrases: absolute Galois group, Galois cohomology, descending central sequence, W-group

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