Quotients of absolute Galois groups which determine the entire Galois cohomology

被引：37
|
作者：
Chebolu, Sunil K. [2 ]
Efrat, Ido [1 ]
Minac, Jan [3 ]
机构：
[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel
[2] Illinois State Univ, Dept Math, Normal, IL 61790 USA
[3] Univ Western Ontario, Dept Math, London, ON N6A 5B7, Canada
来源：
MATHEMATISCHE ANNALEN | 2012年 / 352卷 / 01期
基金：
以色列科学基金会;
关键词：
PRO-P-GROUPS; BODIES;
D O I：
10.1007/s00208-011-0635-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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*( GF, 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.
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页码：205 / 221
页数：17
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