Abstract
TextWe use Massey products and their relations to unipotent representations to parametrize and find an explicit formula for the number of Galois extensions of a given local field with the prescribed Galois group U4(Fp) consisting of unipotent four by four matrices over Fp. Further applications of this method involve the counting of certain Galois extensions with restricted ramifications, and counting the numbers of Galois U4(Fp)-extensions of some other fields. For each Demushkin pro-p-group, we find a very simple version of the condition when the n-fold Massey product of one-dimensional cohomological elements of G with coefficients in Fp, is defined. As an easy consequence, we determine those Un(Fp) which occur as an epimorphic image of any given Demushkin group. VideoFor a video summary of this paper, please visit https://youtu.be/okuEVNNuczc.
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