Quotients of absolute Galois groups which determine the entire Galois cohomology

Sunil K. Chebolu; Ido Efrat; Ján Mináč

doi:10.1007/s00208-011-0635-6

Quotients of absolute Galois groups which determine the entire Galois cohomology

Sunil K. Chebolu, Ido Efrat, Ján Mináč

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

Abstract

For a 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.

Original language	English
Pages (from-to)	205-221
Number of pages	17
Journal	Mathematische Annalen
Volume	352
Issue number	1
DOIs	https://doi.org/10.1007/s00208-011-0635-6
State	Published - 1 Jan 2012

ASJC Scopus subject areas

General Mathematics

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10.1007/s00208-011-0635-6

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abstract = "For a 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.",

author = "Chebolu, {Sunil K.} and Ido Efrat and J{\'a}n Min{\'a}{\v c}",

note = "Funding Information: Sunil Chebolu was supported by a New Faculty Initiative Grant at Illinois State University. Ido Efrat was supported by the Israel Science Foundation (grant No. 23/09). J{\'a}n Min{\'a}{\v c} was supported in part by National Sciences and Engineering Council of Canada grant R0370A01.",

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AU - Efrat, Ido

AU - Mináč, Ján

N1 - Funding Information: Sunil Chebolu was supported by a New Faculty Initiative Grant at Illinois State University. Ido Efrat was supported by the Israel Science Foundation (grant No. 23/09). Ján Mináč was supported in part by National Sciences and Engineering Council of Canada grant R0370A01.

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N2 - For a 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.

AB - For a 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.

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Quotients of absolute Galois groups which determine the entire Galois cohomology

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