Immediate and purely wild extensions of valued fields

DOI10.1007/BF01168612zbMath0593.12018OpenAlexW1994166836MaRDI QIDQ1076077

Matthias Pank, Franz-Viktor Kuhlmann, Peter Roquette

Publication date: 1986

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155126

zbMATH Keywords

uniquenessGalois groupmodel theoryvalued fieldHilbert's ramification theorymaximal immediate extensionsmaximal purely wild extensionssimple transcendental immediate extensions

Mathematics Subject Classification ID

Model theory of fields (12L12) Valued fields (12J10)

Related Items (30)

The valuation theory of deeply ramified fields and its connection with defect extensions ⋮ On the non-uniqueness of maximal purely wild extensions ⋮ Tame distillation and desingularization by \(p\)-alterations ⋮ The algebra and model theory of tame valued fields ⋮ Value groups, residue fields, and bad places of rational function fields ⋮ A Galois-theoretic characterization of \(p\)-adically closed fields ⋮ Valuation theory and its applications. Abstracts from the workshop held October 26 -- November 1, 2014. ⋮ Subfields of algebraically maximal Kaplansky fields ⋮ Unnamed Item ⋮ Valued fields with contractive automorphism and Kaplansky fields ⋮ Spherically complete models of Hensel minimal valued fields ⋮ Defect extensions and a characterization of tame fields ⋮ Characterizing NIP henselian fields ⋮ The model theory of separably tame valued fields ⋮ On maximal immediate extensions of valued fields ⋮ A classification of Artin-Schreier defect extensions and characterizations of defectless fields ⋮ Quantifier elimination in tame infinite p-adic fields ⋮ Algebraic independence of elements in immediate extensions of valued fields ⋮ A Hasse principle for function fields over PAC fields ⋮ Elimination of ramification I: The generalized stability theorem ⋮ Summary on non-Archimedean valued fields ⋮ Elimination of ramification. II: Henselian rationality ⋮ NIP Henselian valued fields ⋮ Tame and purely wild extensions of valued fields ⋮ Every place admits local uniformization in a finite extension of the function field ⋮ The metabelian birational -adic section conjecture for varieties ⋮ A CONJECTURAL CLASSIFICATION OF STRONGLY DEPENDENT FIELDS ⋮ Pro-Pgalois groups of function fields over local fields ⋮ Kaplansky fields andp-algebraically closed fields ⋮ Quantifier elimination for Henselian fields relative to additive and multiplicative congruences

Cites Work

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• Galois cohomology of additive polynomial and \(n\)-th power mappings of fields
• Formally \(p\)-adic fields
• Untersuchungen zur arithmetischen Theorie der Körper. (Die Theorie der Teilbarkeit in allgemeinen Körpern. I-III.)
• Cohomologie galoisienne. Cours au Collège de France, 1962--1963. 3ième éd.
• Zur Verzweigungstheorie der allgemeinen Krullschen Bewertungen
• Valuation theory
• Maximal fields with valuations
• Diophantine Problems Over Local Fields I
• Nonstandard arithmetic
• Endliche Gruppen I

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