Quotients of Absolute Galois Groups Which Determine the Entire Galois Cohomology
نویسنده
چکیده
For prime power q = p and a field F containing a root of unity of order q we show that the Galois cohomology ring H∗(GF , Z/q) is determined by a quotient G [3] F of the absolute Galois group GF related to its descending q-central sequence. Conversely, we show that G [3] F is determined by the lower cohomology of GF . This is used to give new examples of pro-p groups which do not occur as absolute Galois groups of fields.
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