Maps on Ultrametric Spaces, Hensel's Lemma, and Differential Equations Over Valued Fields

DOI10.1080/00927871003789157zbMath1239.12006arXiv1003.5677OpenAlexW2013162281MaRDI QIDQ3090098

Franz-Viktor Kuhlmann

Publication date: 26 August 2011

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

Full work available at URL: https://arxiv.org/abs/1003.5677

zbMATH Keywords

implicit function theoremdifferential fieldHensel's lemmaultrametric spacedifference fielddifferential valuationdifferential Hensel's lemma

Mathematics Subject Classification ID

Differential algebra (12H05) Model theory of fields (12L12) Difference algebra (12H10) Valued fields (12J10) General valuation theory for fields (12J20)

Related Items (20)

Differential-henselianity and maximality of asymptotic valued differential fields ⋮ Quadratic forms and systems of forms in many variables ⋮ On certain Fourier coefficients of Eisenstein series on \(G_2\) ⋮ On valuation independence and defectless extensions of valued fields ⋮ Symmetrically complete ordered sets abelian groups and fields. ⋮ Geometric quadratic Chabauty and \(p\)-adic heights ⋮ Hardy type derivations on fields of exponential logarithmic series ⋮ A closedness theorem and applications in geometry of rational points over Henselian valued fields ⋮ Hardy type derivations on generalised series fields ⋮ 3-torsion and conductor of genus 2 curves ⋮ Coincidence point theorems for ball spaces and their applications ⋮ Surreal numbers with derivation, Hardy fields and transseries: a survey ⋮ Reaching fixed points as limits in subspaces ⋮ Strictly convergent analytic structures ⋮ Liouville closed \(H\)-fields ⋮ A difference version of Nori's theorem ⋮ Explicit quadratic Chabauty over number fields ⋮ Construction of ball spaces and the notion of continuity ⋮ A generic approach to measuring the strength of completeness/compactness of various types of spaces and ordered structures ⋮ The differential rank of a differential-valued field

Cites Work

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• The Banach fixed point theorem for ultrametric spaces
• Differential valuations
• The common point theorem for ultrametric spaces
• Fixed points, combs and generalized power series
• The elementary theory of restricted analytic fields with exponentiation
• A general Hensel's lemma
• A model complete theory of valued D-fields
• Elementary properties of power series fields over finite fields
• Note on a result of Krull
• On the Value Group of a Differential Valuation
• The real field with convergent generalized power series
• Logarithmic-Exponential Power Series
• Logarithmic-exponential series

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