Work

Artin–schreier Extensions and Combinatorial Complexity in Henselian Valued Fields

Year: 2024

Type: article

Abstract: We give explicit formulas witnessing IP, IP $_{\!n}$ , or TP2 in fields with Artin–Schreier extensions. We use them to control p-extensions of mixed characteristic henselian valued fields, allowing us most notably to generalize to the NIP $_{\!n}$ context one way of Anscombe–Jahnke’s classification of NIP henselian valued fields. As a corollary, we obtain that NIP $_{\!n}$ henselian valued fields with NIP residue field are NIP. We also discuss tameness results for NTP2 henselian valued fields.

Source: Journal of Symbolic Logic

DOI: 10.1017/jsl.2024.34

Author: BLAISE BOISSONNEAU

Institution: Académie de Paris

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutscher Akademischer Austauschdienst, Daimler und Benz Stiftung

Award: G7392215527