Relations in the maximal pro-𝑝 quotients of absolute Galois groups

Mináč, Ján; Rogelstad, Michael; Tân, Nguyễn

doi:10.1090/tran/8003

Relations in the maximal pro-$p$ quotients of absolute Galois groups
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by Ján Mináč, Michael Rogelstad and Nguyễn Duy Tân PDF

Trans. Amer. Math. Soc. 373 (2020), 2499-2524 Request permission

Abstract:

We observe that some fundamental constructions in Galois theory can be used to obtain interesting restrictions on the structure of Galois groups of maximal $p$-extensions of fields containing a primitive $p$-th root of unity. This is an extension of some significant ideas of Demushkin, Labute, and Serre from local fields to all fields containing a primitive $p$-th root of unity. Our techniques use certain natural simple Galois extensions together with some considerations in Galois cohomology and Massey products.

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