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For a henselian valued field $(K,v)$ we establish a complete parallelism between the arithmetic properties of irreducible polynomials $F\in K[x]$, encoded by their Okutsu frames, and the valuation-theoretic properties of their induced valuations $v_F
Externí odkaz:
http://arxiv.org/abs/2111.02811
For an arbitrary valued field $(K,v)$ and a given extension $v(K^*)\hookrightarrow\Lambda$ of ordered groups, we analyze the structure of the tree formed by all $\Lambda$-valued extensions of $v$ to the polynomial ring $K[x]$. As an application, we f
Externí odkaz:
http://arxiv.org/abs/2107.09813
Publikováno v:
Journal of Algebra. 614:71-114
For an arbitrary valued field $(K,v)$ and a given extension $v(K^*)\hookrightarrow\Lambda$ of ordered groups, we analyze the structure of the tree formed by all $\Lambda$-valued extensions of $v$ to the polynomial ring $K[x]$. As an application, we f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::54dda21503860eb1327b282dd3e0d91f
https://doi.org/10.1016/j.jalgebra.2022.09.014
https://doi.org/10.1016/j.jalgebra.2022.09.014
Autor:
Michel Vaquié
Publikováno v:
Bulletin of the London Mathematical Society
Bulletin of the London Mathematical Society, 2020, 52 (5), pp.977-992. ⟨10.1112/blms.12378⟩
Bulletin of the London Mathematical Society, London Mathematical Society, 2020, 52 (5), pp.977-992. ⟨10.1112/blms.12378⟩
Bulletin of the London Mathematical Society, 2020, 52 (5), pp.977-992. ⟨10.1112/blms.12378⟩
Bulletin of the London Mathematical Society, London Mathematical Society, 2020, 52 (5), pp.977-992. ⟨10.1112/blms.12378⟩
Let K be a field with a valuation $\nu$ and let L = K(x) be a transcendental extension of K, then any valuation $\mu$ of L which extends $\nu$ is determined by its restriction to the polynomial ring K[x]. We know how to associate to this valuation $\
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::51c24992d47f16c03bf916bf322dc798
https://hal.science/hal-03042225
https://hal.science/hal-03042225
Autor:
Vaquié, Michel
Let $(K, \nu)$ be a valued field, the notions of \emph{augmented valuation}, of \emph{limit augmented valuation} and of \emph{admissible family} of valuations enable to give a description of any valuation $\mu$ of $K [x]$ extending $\nu$. In the case
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::805f48ba3942ecb2c9491713abffee48
https://hal-cnrs.archives-ouvertes.fr/hal-02565309/file/valuation-augmentee-et-paire-minimale_05-05-20.pdf
https://hal-cnrs.archives-ouvertes.fr/hal-02565309/file/valuation-augmentee-et-paire-minimale_05-05-20.pdf
Autor:
Michel Vaquié
Publikováno v:
Annales de l'Institut Fourier
Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2008, 58 (7), pp.2503-2541
Annales de l'Institut Fourier, 2008, 58 (7), pp.2503-2541
Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2008, 58 (7), pp.2503-2541
Annales de l'Institut Fourier, 2008, 58 (7), pp.2503-2541
— Let (K, ν) be a valued field and L a finite cyclic extension of K defined by L = K[x]/(P ), then any valuation of L which extends ν defines a pseudo-valuation ζ onK[x] whose kernel is the principal ideal (P ). We know how to associate to ζ a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::39c75c0114d0c67a6b9a8e6da2c1c1e8
https://doi.org/10.5802/aif.2421
https://doi.org/10.5802/aif.2421