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

@article{AFST_2010_6_19_3-4_525_0,
     author = {Aroca, Fuensanta},
     title = {Krull-Tropical Hypersurfaces},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 19},
     number = {3-4},
     year = {2010},
     pages = {525-538},
     doi = {10.5802/afst.1255},
     mrnumber = {2790807},
     zbl = {1223.14069},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2010_6_19_3-4_525_0}
}
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://www.numdam.org/item/AFST_2010_6_19_3-4_525_0/

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