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Preprint Number 1204

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1204. Katharina Dupont, Assaf Hasson, Salma Kuhlmann
Definable Valuations induced by multiplicative subgroups and NIP Fields
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Submission date: 10 April 2017

Abstract:

We study the algebraic implications of the non-independence property (NIP) and variants thereof (dp-minimality) on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a definable henselian valuation. Our results mainly focus on Hahn fields and build up on Will Johnson's preprint dp-minimal fields, arXiv: 1507.02745v1, July 2015.

Mathematics Subject Classification: 03C68

Keywords and phrases: NIP, strong NIP, definable valuations, henselian fields, Hahn fields, dp-minimal fields

Full text arXiv 1704.02910: pdf, ps.


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