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De l’application des méthodes valuatives en algèbre différentielle
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 17 (2008) no. 4, pp. 673-717.

La théorie des valuations née des travaux des géomètres et arithméticiens du XIX ê me siècle, fit une apparition tardive et encore peu connue au XX ê me siècle en algèbre différentielle. Dans cet article, à travers les contributions de nombreux auteurs, nous présentons une synthèse des divers apports de la théorie des valuations à l’étude des équations différentielles. Nous insistons sur le caractère unificateur de la théorie des valuations en illustrant comment elles permettent de mettre en parallèle des résultats de géométrie et d’arithmétique avec des résultats concernant les équations différentielles.

Valuation theory is a classical achievement of the works of geometers and arithmeticians of the nineteen century. In contrast, its apparition in Differential Algebra is far to be well known and only appear in the second half of the twenty century. The aim of this paper is to give an overview of the use of valuations in Differential Algebra. Thanks to the contributions of many autors, we try to show how valuations might help to unify results coming from geometry, arithmetic and differrential equations.

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DOI : https://doi.org/10.5802/afst.1198
@article{AFST_2008_6_17_4_673_0,
     author = {Guillaume Duval},
     title = {De l{\textquoteright}application des m\'ethodes valuatives en alg\`ebre diff\'erentielle},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {673--717},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {6e s{\'e}rie, 17},
     number = {4},
     year = {2008},
     doi = {10.5802/afst.1198},
     zbl = {1160.13001},
     mrnumber = {2499775},
     language = {fr},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1198/}
}
Guillaume Duval. De l’application des méthodes valuatives en algèbre différentielle. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 17 (2008) no. 4, pp. 673-717. doi : 10.5802/afst.1198. https://afst.centre-mersenne.org/articles/10.5802/afst.1198/

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