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VALUATION AUGMENTÉE ET PAIRE MINIMALE

Abstract : Let (K, ν) be a valued field, the notions of augmented valuation, of limit augmented valuation and of admissible family of valuations enable to give a description of any valuation μ of K[x] extending ν. In the case where the field K is algebraically closed, this description is particularly simple and we can reduce it to the notions of minimal pair and pseudo-convergent family. Let (K, ν) be a henselian valued field and ν ̄ the unique extension of ν to the algebraic closure K ̄ of K and let μ be a valuation of K[x] extending ν, we study the extensions μ ̄ from μ to K ̄[x] and we give a description of the valuations μ ̄i of K ̄ [x] which are the extensions of the valuations μi belonging to the admissible family associated with μ.
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https://hal-cnrs.archives-ouvertes.fr/hal-02565309
Contributor : Michel Vaquié <>
Submitted on : Wednesday, March 10, 2021 - 9:05:20 PM
Last modification on : Wednesday, June 9, 2021 - 10:00:11 AM

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  • HAL Id : hal-02565309, version 2
  • ARXIV : 2005.03298

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Michel Vaquié. VALUATION AUGMENTÉE ET PAIRE MINIMALE. 2021. ⟨hal-02565309v2⟩

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