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Comptes Rendus Mathématique
Volume 346, n° 3-4
pages 129-133 (février 2008)
Doi : 10.1016/j.crma.2008.01.004
Received : 12 July 2007 ;  accepted : 15 January 2008
Classes d’homotopie de fractions rationnelles
Homotopy classes of rational functions
 

Christophe Cazanave
Laboratoire d’analyse, géométrie et applications UMR 7539, institut Galilée, université Paris 13, 99, avenue J.B. Clément, 93430 Villetaneuse, France 

Résumé

Soient k un corps de caractéristique différente de 2 et   un entier ; on munit l’ensemble des classes d’homotopie « algébrique » de fractions rationnelles pointées de degré n à coefficients dans k d’une structure de monoïde gradué par n et l’on construit un isomorphisme entre ce monoïde et celui des orbites sous l’action de   de formes bilinéaires symétriques non dégénérées sur  , muni de la somme orthogonale. Pour citer cet article : C. Cazanave, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
Abstract

Let k be a field of characteristic not 2 and   be an integer; we show that the set of “algebraic” homotopy classes of rational functions of degree n with coefficients in k can be endowed with a graded monoid structure. Moreover, there is an isomorphism between this monoid and the monoid of orbits under the action of   of non-degenerate symmetric bilinear forms on  , endowed with the orthogonal sum. To cite this article: C. Cazanave, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.

 La présente Note doit beaucoup à Jean Lannes, tant pour le fond que pour la forme ; je lui exprime ici ma plus sincère gratitude.



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