Extensions of valuations to rational function fields over completions

DOI10.1002/mana.202200178arXiv2203.04801OpenAlexW4383273342MaRDI QIDQ6049400

Arpan Dutta

Publication date: 17 October 2023

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.04801

zbMATH Keywords

minimal pairsvaluationkey polynomialsimplicit constant fieldspseudo Cauchy sequencescompletion of valuationsextension of valuation to rational function fields

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Quantum computation (81P68) Density theorems (11R45) Special sequences and polynomials (11B83) Real rational functions (26C15)

Cites Work

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• All valuations on K(X)
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• Untersuchungen zur arithmetischen Theorie der Körper. (Die Theorie der Teilbarkeit in allgemeinen Körpern. I-III.)
• On the implicit constant fields and key polynomials for valuation algebraic extensions
• Minimal pairs, minimal fields and implicit constant fields
• Maximal fields with valuations. I, II
• Extension d’une valuation
• Value groups, residue fields, and bad places of rational function fields
• Valuation theoretic and model theoretic aspects of local uniformization
• Minimal pairs, inertia degrees, ramification degrees and implicit constant fields

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