On groups and fields definable in 1-h-minimal fields

Juan Pablo Acosta; Assaf Hasson

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arXiv · 2303.01127

On groups and fields definable in 1-h-minimal fields

Juan Pablo Acosta·Assaf Hasson

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Abstract

We show that an infinite group $G$ definable in a $1$-h-minimal field admits a strictly $K$-differentiable structure with respect to which $G$ is a (weak) Lie group, and show that definable local subgroups sharing the same Lie algebra have the same germ at the identity. We conclude that infinite fields definable in $K$ are definably isomorphic to finite extensions of $K$ and that $1$-dimensional groups definable in $K$ are finite-by-abelian-by-finite. Along the way we develop the basic theory of definable weak $K$-manifolds and definable morphisms between them.

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BibTeX RIS

Juan Pablo Acosta, Assaf Hasson. 2023-03-02. On groups and fields definable in 1-h-minimal fields. https://arxiv.org/abs/2303.01127

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