Higher Massey products in the cohomology of mild pro-p-groups
Translating results due to J. Labute into group cohomological language, A. Schmidt proved that a finitely presented pro-p-group G is mild and hence of cohomological dimension cdG=2 if H1(G,Fp)=U⊕V as Fp-vector space and the cup-product H1(G,Fp)⊗H1(G,Fp)→H2(G,Fp) maps U⊗V surjectively onto H2(G,Fp) a...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2015
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| In: |
Journal of algebra
Year: 2014, Jahrgang: 422, Pages: 788-820 |
| ISSN: | 1090-266X |
| DOI: | 10.1016/j.jalgebra.2014.07.023 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jalgebra.2014.07.023 Verlag, lizenzpflichtig, Volltext: http://www.sciencedirect.com/science/article/pii/S0021869314004384 
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| Verfasserangaben: | Jochen Gärtner, Mathematisches Institut, Universität Heidelberg |
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| 520 | |a Translating results due to J. Labute into group cohomological language, A. Schmidt proved that a finitely presented pro-p-group G is mild and hence of cohomological dimension cdG=2 if H1(G,Fp)=U⊕V as Fp-vector space and the cup-product H1(G,Fp)⊗H1(G,Fp)→H2(G,Fp) maps U⊗V surjectively onto H2(G,Fp) and is identically zero on V⊗V. This has led to important results in the study of p-extensions of number fields with restricted ramification, in particular in the case of tame ramification. In this paper, we extend Labute's theory of mild pro-p-groups with respect to weighted Zassenhaus filtrations and prove a generalization of the above result for higher Massey products which allows to construct mild pro-p-groups with defining relations of arbitrary degree. We apply these results to one-relator pro-p-groups and obtain some new evidence of an open question due to Serre. | ||
| 534 | |c 2014 | ||
| 650 | 4 | |a Cohomological dimension | |
| 650 | 4 | |a Massey products | |
| 650 | 4 | |a Mild pro;groups | |
| 650 | 4 | |a One-relator pro;groups | |
| 650 | 4 | |a Restricted Lie algebras | |
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