Quotients of absolute Galois groups which determine the entire Galois cohomology

By Sunil K. Chebolu, Ido Efrat, Ján Minác. 2009

65 citations recorded by the source corpus.

For a prime power q = pd and a field F containing a root of unity of order q we show that the Galois cohomology ring $${H^*(G_F,\mathbb{Z}/q)}$$ is determined by a quotient $${G_F^{[3]}}$$ of the absolute Galois group GF related to its descending q-central sequence. Conversely, we show that $${G_F^{[3]}}$$ 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/80d9d3f7c98d06cd6903425016904d219a56c6b3

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In Geometry and Topology

1. Ido Efrat
2. Eliyahu Matzri
3. Ján Minác

In Mathematical Physics

1. Ido Efrat
2. Eliyahu Matzri
3. Ján Minác

Citations in the corpus

• On the descending central sequence of absolute Galois groups (2008, background): “atic forms of F ([MSp90], [MSp96]) as well as some non-trivial valuations [MMS04]. Further, it encodes the entire mod 2 Galois cohomology ring of GF [AKM99, Th. 3.14]. In a joint work with S. Chebolu [CEM], we show that GF/G (3) F can be in fact thought of as a group-theoretic analog of the Galois c”
• Triple Massey products and Galois theory (2013, unknown): “re the generating relation is a product of commutators between generators and p-powers of generators. (If GF(p) for a local field is not a Demushkin group, then it is free pro-p.) Already in the paper [CEM], Section 9, it was shown that G := S/h[[x1,x2],x3]i, where S is a free pro-2-group on generato”
• Triple Massey products and absolute Galois groups (2014, result): “G F) is generated by its degree 1 elements, and its relations originate from the degree 2 component. This can be used to rule out many more profinite groups from being absolute Galois groups of fields ([CEM12], [EM11b]). In fact, the Artin– Schreier restriction about the torsion also follows from the ”
• The Zassenhaus filtration, Massey Products, and Representations of Profinite Groups (2013, background): “rite H2(S/N) n−Massey for the image of this map. Example 8.5. For n= 2 and χ1,χ2 ∈H1(S/N) we have by construction hχ1,χ2i= −χ1 ∪χ2 ∈H2(S/N), where ∪denotes the cup product. Thus in the terminology of [CEM12], H2(S/N) 2−Massey = H 2(S/N) dec. For a ∈A we may consider ǫ(a),Z/m ∈H1(S) also as an elemen”