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arXiv · 2301.10342

Two-step nilpotent extensions are not anabelian

Peter Koymans·Carlo Pagano
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Abstract

We prove the existence of two non-isomorphic number fields $K$ and $L$ such that the maximal two-step nilpotent quotients of their absolute Galois groups are isomorphic. In particular, one may take $K$ and $L$ to be any of the imaginary quadratic number fields of discriminant -11, -19, -43, -67, -163. Furthermore, we give an explicit combinatorial description of these Galois groups in terms of a generalization of the Rado graph. A critical ingredient in our proofs is the back-and-forth method from model theory.

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Peter Koymans, Carlo Pagano. 2023-01-24. Two-step nilpotent extensions are not anabelian. https://arxiv.org/abs/2301.10342

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