The Zassenhaus filtration, Massey products, and representations of profinite groups
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Publication:2509965
DOI10.1016/J.AIM.2014.07.006zbMATH Open1346.20027arXiv1301.0896OpenAlexW2962920382MaRDI QIDQ2509965
Author name not available (Why is that?)
Publication date: 31 July 2014
Published in: (Search for Journal in Brave)
Abstract: We consider the p-Zassenhaus filtration (G_n) of a profinite group G. Suppose that G=S/N for a free profinite group S and a normal subgroup N of S contained in S_n. Under a cohomological assumption on the n-fold Massey products (which holds e.g., if the p-cohomological dimension of G is at most 1), we prove that G_{n+1} is the intersection of all kernels of upper-triangular unipotent (n+1)-dimensional representations of G over mathbb F_p. This extends earlier results by Minac, Spira, and the author on the structure of absolute Galois groups of fields.
Full work available at URL: https://arxiv.org/abs/1301.0896
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