Pseudo T-closed fields

Samaria Montenegro; Silvain Rideau-Kikuchi

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arXiv · 2304.10433

Pseudo T-closed fields

Samaria Montenegro·Silvain Rideau-Kikuchi

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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" 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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BibTeX RIS

Samaria Montenegro, Silvain Rideau-Kikuchi. 2023-04-20. Pseudo T-closed fields. https://arxiv.org/abs/2304.10433

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