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VALUATION AUGMENTÉE ET PAIRE MINIMALE
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.
https://hal-cnrs.archives-ouvertes.fr/hal-02565309
Contributor : Michel Vaquié Connect in order to contact the contributor
Submitted on : Wednesday, March 10, 2021 - 9:05:20 PM
Last modification on : Monday, July 4, 2022 - 8:42:50 AM
Contributor : Michel Vaquié Connect in order to contact the contributor
Submitted on : Wednesday, March 10, 2021 - 9:05:20 PM
Last modification on : Monday, July 4, 2022 - 8:42:50 AM
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