no. 3
Sign functions of imaginary quadratic fields and applications
[Fonction signe des corps quadratiques imaginaires et applications]
Oukhaba, Hassan1
1 Université de Franche-Comte, laboratoire de mathématique, 16 Route de Gray, 25030 Besançon cedex (France)
Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 753-772.

Nous proposons une définition du signe pour les corps quadratiques imaginaires. Nous donnons un exemple de telles fonctions et l'utilisons pour définir de nouveaux invariants qui sont racines des invariants de Ramachandra classiques. D'autre part nous introduisons les distributions ordinaires signées et calculons leur cohomologie à l'aide de la theéorie d'Anderson dite du double complexe.

We propose a definition of sign of imaginary quadratic fields. We give an example of such functions, and use it to define new invariants that are roots of the classical Ramachandra invariants. Also we introduce signed ordinary distributions and compute their signed cohomology by using Anderson's theory of double complex.

DOI : 10.5802/aif.2113
Classification : 11G16, 14K22, 11R21
Keywords: sign function, narrow ray class field, Shimura reciprocity law, ordianary $s$-ditributions, Anderson’s resolution, spectrales sequences
Mot clés : fonction signe, corps de rayon restreints, loi de réciprocité de Shimura, $s$-distributions ordinaires, résolution d’Anderson, suites spectrales
Oukhaba, Hassan 1

1 Université de Franche-Comte, laboratoire de mathématique, 16 Route de Gray, 25030 Besançon cedex (France) 
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Oukhaba, Hassan. Sign functions of imaginary quadratic fields and applications. Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 753-772. doi : 10.5802/aif.2113. http://archive.numdam.org/articles/10.5802/aif.2113/

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