On definable groups in dp-minimal topological fields equipped with a generic derivation

2025/05/11 by Françoise Point, Point, Françoise
Computer Science · Mathematics · #03C60 #12H05 #12L12 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2505.07044

openalex publication_date 2025/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T be a complete, model-complete, geometric dp-minimal L-theory of topological fields of characteristic 0 and let T(∂) be the theory of expansions of models of T by a derivation ∂. We assume that T(∂) has a model-companion T_∂. Let Γ be a finite-dimensional L_∂-definable group in a model of T_∂. Then we show that Γ densely and definably embeds in an L-definable group G. Further, using a C¹-cell decomposition result, we show that Γ densely and definably embeds in a definable D-group, generalizing the classical construction of Buium of algebraic D-groups and extending for that class of fields, results obtained in arXiv:2208.08293, arXiv:2305.16747.

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