共查询到20条相似文献,搜索用时 15 毫秒
1.
《Journal of Pure and Applied Algebra》2022,226(9):107039
In this paper we identify a class of profinite groups (totally torsion free groups) that includes all separable Galois groups of fields containing an algebraically closed subfield, and demonstrate that it can be realized as an inverse limit of torsion free virtually finitely generated abelian (tfvfga) profinite groups. We show by examples that the condition is quite restrictive. In particular, semidirect products of torsion free abelian groups are rarely totally torsion free. The result is of importance for K-theoretic applications, since descent problems for tfvfga groups are relatively manageable. 相似文献
2.
Inga Blomer Peter A. Linnell Thomas Schick 《Proceedings of the American Mathematical Society》2008,136(10):3449-3459
In this paper we compute the Galois cohomology of the pro- completion of primitive link groups. Here, a primitive link group is the fundamental group of a tame link in whose linking number diagram is irreducible modulo (e.g. none of the linking numbers is divisible by ).
The result is that (with -coefficients) the Galois cohomology is naturally isomorphic to the -cohomology of the discrete link group.
The main application of this result is that for such groups the Baum-Connes conjecture or the Atiyah conjecture are true for every finite extension (or even every elementary amenable extension), if they are true for the group itself.
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We use étale cohomology to prove some explicit results on the Galois cohomology of ideal class groups.
Received: 3 May 2007 相似文献
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Jochen Koenigsmann 《Israel Journal of Mathematics》2002,127(1):93-129
By two well-known results, one of Ax, one of Lubotzky and van den Dries, a profinite group is projective iff it is isomorphic
to the absolute Galois group of a pseudo-algebraically closed field. This paper gives an analogous characterization of relatively
projective profinite groups as absolute Galois groups of regularly closed fields.
Dedicated to Yuri Ershov on the occasion of his 60-th birthday
Heisenberg-Stipendiat der Deutschen Forschungsgemeinschaft (KO 1962/1-1). 相似文献
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Ivo M. Michailov 《Central European Journal of Mathematics》2011,9(2):403-419
In this paper we develop some new theoretical criteria for the realizability of p-groups as Galois groups over arbitrary fields. We provide necessary and sufficient conditions for the realizability of 14
of the 22 non-abelian 2-groups having a cyclic subgroup of index 4 that are not direct products of groups. 相似文献
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Elaborating on techniques of Bayer-Fluckiger and Parimala, we prove the following strong version of Serre’s Conjecture II for classical groups: let G be a simply connected absolutely simple group of outer type An or of type Bn, Cn or Dn (non trialitarian) defined over an arbitrary field F. If the separable dimension of F is at most 2 for every torsion prime of G, then every G-torsor is trivial. 相似文献
9.
Jochen Koenigsmann 《Inventiones Mathematicae》2001,144(1):1-22
We show that solvable absolute Galois groups have an abelian normal subgroup such that the quotient is the direct product
of two finite cyclic and a torsion-free procyclic group. In particular, solvable absolute Galois groups are metabelian. Moreover,
any field with solvable absolute Galois group G admits a non-trivial henselian valuation, unless each Sylow-subgroup of G is either procyclic or isomorphic to Z
2⋊Z/2Z. A complete classification of solvable absolute Galois groups (up to isomorphism) is given.
Oblatum 22-IV-1998 & 1-IX-2000?Published online: 30 October 2000 相似文献
10.
Ivo M. Michailov 《Central European Journal of Mathematics》2011,9(6):1333-1343
In [Michailov I.M., On Galois cohomology and realizability of 2-groups as Galois groups, Cent. Eur. J. Math., 2011, 9(2), 403–419] we calculated the obstructions to the realizability as Galois groups of 14 non-abelian groups of order 2 n , n ≥ 4, having a cyclic subgroup of order 2 n−2, over fields containing a primitive 2 n−3th root of unity. In the present paper we obtain necessary and sufficient conditions for the realizability of the remaining 8 groups that are not direct products of smaller groups. 相似文献
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《Journal of Pure and Applied Algebra》2023,227(4):107262
Let p be a prime. We study pro-p groups of p-absolute Galois type, as defined by Lam–Liu–Sharifi–Wake–Wang. We prove that the pro-p completion of the right-angled Artin group associated to a chordal simplicial graph is of p-absolute Galois type, and moreover it satisfies a strong version of the Massey vanishing property. Also, we prove that Demushkin groups are of p-absolute Galois type, and that the free pro-p product — and, under certain conditions, the direct product — of two pro-p groups of p-absolute Galois type satisfying the Massey vanishing property, is again a pro-p group of p-absolute Galois type satisfying the Massey vanishing property. Consequently, there is a plethora of pro-p groups of p-absolute Galois type satisfying the Massey vanishing property that do not occur as absolute Galois groups. 相似文献
13.
Andrei Minchenko 《代数通讯》2013,41(12):5094-5100
For a partial differential field K, we show that the triviality of the first differential Galois cohomology of every linear differential algebraic group over K is equivalent to K being algebraically, Picard–Vessiot, and linearly differentially closed. This cohomological triviality condition is also known to be equivalent to the uniqueness up to an isomorphism of a Picard–Vessiot extension of a linear differential equation with parameters. 相似文献
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We extend the framework of entire cyclic cohomology to the equivariant context.Supported in part by the Department of Energy under Grant DE-FG02-88ER25065. 相似文献
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For finite field extensions of the field of Henselian p-adic rational numbers necessary and sufficient conditions are given which state that the fields have isomorphic absolute Galois groups; it is thereby supposed that a p-th root of unity (a 4-th when p = 2) belongs to the fields. Also examples are discussed. 相似文献
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Oblatum 8-XII-1994 7-III-1995 相似文献
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Donald L McQuillan 《Journal of Number Theory》1976,8(4):438-445
Let R be a Dedekind domain, G a finite group of automorphisms of R, and A an ambiguous ideal of R i.e., σA = A for all σ ∈ G. The Tate groups Hn(G, A) are considered as RG-modules. A localization theorem is proved and the precise RG-module structure determined in a particular case. In addition some remarks are made concerning cohomological triviality. 相似文献