Minimal pairs, inertia degrees, ramification degrees and implicit constant fields

DOI10.1080/00927872.2022.2078833zbMath1498.13010arXiv2111.13641OpenAlexW3214771362MaRDI QIDQ5097426

Arpan Dutta

Publication date: 23 August 2022

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.13641

zbMATH Keywords

minimal pairsvaluationramification theoryimplicit constant fieldsvaluation transcendental extensionsextensions of valuation to rational function fields

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Non-Archimedean valued fields (12J25) General valuation theory for fields (12J20)

Related Items (2)

Extensions of valuations to rational function fields over completions ⋮ On the implicit constant fields and key polynomials for valuation algebraic extensions

Cites Work

• Unnamed Item
• A theorem of characterization of residual transcendental extensions of a valuation
• Eliminating tame ramification generalizations of Abhyankar's lemma
• Minimal pairs of definition of a residual transcendental extension of a valuation
• Extending valuations to the field of rational functions using pseudo-monotone sequences
• On the ranks and implicit constant fields of valuations induced by pseudo monotone sequences
• Minimal pairs, minimal fields and implicit constant fields
• Elimination of ramification I: The generalized stability theorem
• Value groups, residue fields, and bad places of rational function fields

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