Higher Massey products in the cohomology of mild pro-p-groups

• Verfasst von: Gärtner, Jochen [VerfasserIn]
• Titel: Higher Massey products in the cohomology of mild pro-p-groups
• Verf.angabe: Jochen Gärtner, Mathematisches Institut, Universität Heidelberg
• Jahr: 2015
• Jahr des Originals: 2014
• Umfang: 33 S.
• Fussnoten: Available online 23 September 2014 ; Gesehen am 19.06.2020
• Titel Quelle: Enthalten in: Journal of algebra
• Ort Quelle: San Diego, Calif. : Elsevier, 1964
• Jahr Quelle: 2015
• Band/Heft Quelle: 422(2015), Seite 788-820
• ISSN Quelle: 1090-266X
• DOI: doi:10.1016/j.jalgebra.2014.07.023
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Cohomological dimension
• Sach-SW: Massey products
• Sach-SW: Mild pro;groups
• Sach-SW: One-relator pro;groups
• Sach-SW: Restricted Lie algebras
• K10plus-PPN: 1701134217

Abstract

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.