The Zassenhaus filtration, Massey Products, and Representations of Profinite Groups

By Ido Efrat. 2013

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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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/08549e888ca6b0c4bfbeaa9c168d6198d3fdac45