Taylor towers for Γ-modules
[Approximation de Taylor pour les Γ-modules]
Richter, Birgit1
1 Mathematisches Institut der Universität Bonn, Beringsstrasse 1, 53115 Bonn (Germany)
Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 995-1023.

Soient Γ la catégorie des ensembles finis pointés et F un Γ-module, donc un foncteur de la catégorie Γ vers une catégorie des modules sur un anneau commutatif. Nous développons une approximation de Taylor pour ces foncteurs. On démontre dans cet article qu’il y a une description explicite de l’homologie d’approximation de Taylor pour les Γ-modules. Nous construisons une suite spectrale pour l’homologie des fibres homotopiques dans cette tour de Taylor et nous faisons des calculs en caractéristique zéro, qui donnent une application pour l’homologie de Hochschild d’ordre supérieur.

We consider Taylor approximation for functors from the small category of finite pointed sets Γ to modules and give an explicit description for the homology of the layers of the Taylor tower. These layers are shown to be fibrant objects in a suitable closed model category structure. Explicit calculations are presented in characteristic zero including an application to higher order Hochschild homology. A spectral sequence for the homology of the homotopy fibres of this approximation is provided.

DOI : 10.5802/aif.1842
Classification : 18A25, 18G10, 55P65
Keywords: Taylor tower, cubical construction, dual of the Steenrod algebra
Mot clés : approximation de Taylor, construction cubique, dual de l'algèbre de Steenrod
Richter, Birgit 1

1 Mathematisches Institut der Universität Bonn, Beringsstrasse 1, 53115 Bonn (Germany) 
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Richter, Birgit. Taylor towers for $\Gamma $-modules. Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 995-1023. doi : 10.5802/aif.1842. http://www.numdam.org/articles/10.5802/aif.1842/

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