Let p be a prime. We produce two new families of pro-p groups which are not realizable as absolute Galois groups of fields. To prove this we use the 1-smoothness property of absolute Galois pro-p groups. Moreover, we show in these families one has one-relator pro-p groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of Rost-Voevodsky Theorem), or the vanishing of Massey products in Galois cohomology.

Two families of pro-p groups that are not Absolute Galois Groups

Quadrelli, C
2022-01-01

Abstract

Let p be a prime. We produce two new families of pro-p groups which are not realizable as absolute Galois groups of fields. To prove this we use the 1-smoothness property of absolute Galois pro-p groups. Moreover, we show in these families one has one-relator pro-p groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of Rost-Voevodsky Theorem), or the vanishing of Massey products in Galois cohomology.
2022
https://www.degruyter.com/document/doi/10.1515/jgth-2020-0186/html
Galois cohomology; Maximal pro-p Galois groups; Absolute Galois groups; Kummerian pro-p pairs; Massey products.
Quadrelli, C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2129360
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