Let p be a prime. We prove that certain amalgamated free pro-p products of Demushkin groups with pro-p-cyclic amalgam cannot give rise to a 1-cyclotomic oriented pro-p group, and thus do not occur as maximal pro-p Galois groups of fields containing a root of 1 of order p. We show that other cohomological obstructions which are used to detect pro-p groups that are not maximal pro-p Galois groups - the quadraticity of Z/pZ-cohomology and the vanishing of Massey products - fail with the above pro-p groups. Finally, we prove that the Minač-Tân pro-p group cannot give rise to a 1-cyclotomic oriented pro-p group, and we conjecture that every 1-cyclotomic oriented pro-p group satisfy the strong n-Massey vanishing property for n>2.

Chasing maximal pro-p Galois groups via 1-cyclotomicity

claudio quadrelli
2024-01-01

Abstract

Let p be a prime. We prove that certain amalgamated free pro-p products of Demushkin groups with pro-p-cyclic amalgam cannot give rise to a 1-cyclotomic oriented pro-p group, and thus do not occur as maximal pro-p Galois groups of fields containing a root of 1 of order p. We show that other cohomological obstructions which are used to detect pro-p groups that are not maximal pro-p Galois groups - the quadraticity of Z/pZ-cohomology and the vanishing of Massey products - fail with the above pro-p groups. Finally, we prove that the Minač-Tân pro-p group cannot give rise to a 1-cyclotomic oriented pro-p group, and we conjecture that every 1-cyclotomic oriented pro-p group satisfy the strong n-Massey vanishing property for n>2.
2024
2024
https://link.springer.com/article/10.1007/s00009-024-02598-0
Galois cohomology, maximal pro-p Galois groups, Cyclotomic oriented pro-p groups, absolutely torsion-free pro-p groups, Massey products.
Quadrelli, Claudio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2166392
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