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Original Articles

QUELQUES CALCULS DE COHOMOLOGIE DE COMPOSITIONS DE PUISSANCES SYMÉTRIQUES

Pages 3351-3382 | Received 01 Feb 2001, Published online: 01 Feb 2007
 

ABSTRACT

The main purpose of this paper is to compute the Ext-groups and , in the category of functors from finite -vector spaces to all -vect or spaces. This computation gives an approach to the more general computation of . The two main tools are a comparison theorem between Ext-groups in the category and Ext-groups in the category of strict polynomial functors, and the exactness modulo of the post-composition. This means that the homology appearing when applying a functor to a short exact sequence is in the kernel of .

RÉSUMÉ

Cet article vise principalement à calculer les groupes et , dans la catégorie des foncteurs des espaces vectoriels finis sur vers tous les espaces vectoriels. Ce calcul spécifique fournit une approche de celui de . Les deux outils essentiels sont, d'une part, un théorème de comparaison entre les groupes Ext dans la catégorie et dans la catégorie des foncteurs polynomiaux , et d'autre part l' de la post-composition: l'homologie apparaissant lorsqu'on applique un foncteur à une suite exacte courte appartient au noyau de .

Acknowledgments

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