Submission date: 20 April 2023

Abstract:

Pseudo algebraically closed, pseudo real closed, and pseudo p-adically closed fields are examples of unstable fields that share many similarities, but have mostly been studied separately. In this text, we propose a unified framework for studying them: the class of pseudo T-closed fields, where T is an enriched theory of fields. These fields verify a “local-global&148; principle for the existence of points on varieties with respect to models of T. This approach also enables a good description of some fields equipped with multiple V-topologies, particularly pseudo algebraically closed fields with a finite number of valuations. One important result is a (model theoretic) classification result for bounded pseudo T-closed fields, in particular we show that under specific hypotheses on T, these fields are NTP_2 of finite burden.

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Full text arXiv 2304.10433: pdf, ps.