Submission date: 14 February 2024

Abstract:

This paper aims at developing model-theoretic tools to study interpretable fields and definably amenable groups, mainly in NIP or 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 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.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 2402.09143: pdf, ps.