Quotients of absolute Galois groups which determine the entire Galois cohomology

2009/05/09 by Chebolu, Sunil K., Efrat, Ido, Mináč, Ján · 1 citation
#12E30 #12F10 (Secondary) #12G05 (Primary) #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0905.1364

Abstract

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,\dbZ/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.

Cited by

• Cofinality of Galois Cohomology within Purely Quadratic Graded Algebras

Related

• Galois groups and cohomological functors
• Detecting pro-p-groups that are not absolute Galois groups, expanded version
• Relations in the maximal pro-p quotients of absolute Galois groups
• On the descending central sequence of absolute Galois groups
• The first two cohomology groups of some Galois groups