Semisimple groups interpretable in various valued fields

2023/09/06 by Yatir Halevi, Halevi, Yatir, Assaf Hasson +3
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2309.02727

openalex publication_date 2023/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study infinite groups interpretable in power bounded T-convex, V-minimal or p-adically closed fields. We show that if G is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups) then, up to a finite index subgroup, it is definably isogenous to a group G₁× G₂, where G₁ is a K-linear group and G₂ is a k-linear group. The analysis is carried out by studying the interaction of G with four distinguished sorts: the valued field K, the residue field k, the value group Γ, and the closed 0-balls K/O.

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