Krull-Tropical Hypersurfaces
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 3-4, pp. 525-538.

The concepts of tropical semiring and tropical hypersurface, are extended to the case of an arbitrary ordered group. Then, we define the tropicalization of a polynomial with coefficients in a Krull-valued field. After a close study of the properties of the operator “tropicalization" we conclude with an extension of Kapranov’s theorem to algebraically closed fields together with a valuation over an ordered group.

Les concepts de « semi-anneau » et d’« hypersurface tropicale » sont étendus au cas des groupes ordonnés quelconques. Ensuite, nous definissons la « tropicalisation » d’un polynôme à coefficients dans un corps valué. Après une étude détaillée de l’opérateur de tropicalisation, nous donnons une généralisation du théorème de Kapranov aux corps algébriquement clos munis d’une valuation à valeurs dans un groupe ordonné.

DOI: 10.5802/afst.1255
Aroca, Fuensanta 1

1 Instituto de Matemáticas (Unidad Cuernavaca) Universidad Nacional Autónoma de México. A.P. 273, Admon. de correos #3 C.P. 62251 Cuernavaca, Morelos
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Aroca, Fuensanta. Krull-Tropical Hypersurfaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 3-4, pp. 525-538. doi : 10.5802/afst.1255. http://archive.numdam.org/articles/10.5802/afst.1255/

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