Soient la catégorie des ensembles finis pointés et un -module, donc un foncteur de la catégorie 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 -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 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.
Keywords: Taylor tower, cubical construction, dual of the Steenrod algebra
Mot clés : approximation de Taylor, construction cubique, dual de l'algèbre de Steenrod
@article{AIF_2001__51_4_995_0, author = {Richter, Birgit}, title = {Taylor towers for $\Gamma $-modules}, journal = {Annales de l'Institut Fourier}, pages = {995--1023}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {51}, number = {4}, year = {2001}, doi = {10.5802/aif.1842}, mrnumber = {1849212}, zbl = {0997.18008}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1842/} }
TY - JOUR AU - Richter, Birgit TI - Taylor towers for $\Gamma $-modules JO - Annales de l'Institut Fourier PY - 2001 SP - 995 EP - 1023 VL - 51 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1842/ DO - 10.5802/aif.1842 LA - en ID - AIF_2001__51_4_995_0 ER -
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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