On groups and fields interpretable in $\mathrm{NTP_2}$ fields

Paul Z. Wang

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arXiv · 2402.09143

On groups and fields interpretable in $\mathrm{NTP_2}$ fields

Paul Z. Wang

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Abstract

This paper aims at developing model-theoretic tools to study interpretable fields and definably amenable groups, mainly in $\mathrm{NIP}$ or $\mathrm{NTP_2}$ settings. An abstract theorem constructing definable group homomorphisms from generic data is proved. It relies heavily on a stabilizer theorem of Montenegro, Onshuus and Simon. The main application is a structure theorem for definably amenable groups that are interpretable in algebraically bounded perfect $\mathrm{NTP_2}$ fields with bounded Galois group (under some mild assumption on the imaginaries involved), or in algebraically bounded theories of (differential) NIP fields. These imply a classification of the fields interpretable in differentially closed valued fields, and structure theorems for fields interpretable in finitely ramified henselian valued fields of characteristic $0$, or in NIP algebraically bounded differential fields.

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BibTeX RIS

Paul Z. Wang. 2024-02-14. On groups and fields interpretable in $\mathrm{NTP_2}$ fields. https://arxiv.org/abs/2402.09143

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