Quotients of absolute Galois groups which determine the entire Galois cohomology
2009
Online
report
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.
Comment: 16 pages, Final version, To appear in Mathematische Annalen
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Quotients of absolute Galois groups which determine the entire Galois cohomology
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Autor/in / Beteiligte Person: | Chebolu, Sunil K. ; Efrat, Ido ; Mináč, Ján |
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Veröffentlichung: | 2009 |
Medientyp: | report |
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