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Représentations génériques des groupes linéaires : catégories de foncteurs en grassmanniennes, avec applications à la conjecture artinienne

Abstract : The aim of this work is to study the global structure of the category F of functors between F_2-vector spaces, particularly the artinian conjecture, which is equivalent to the locally noetherian character of F. We show that the tensor product between a finite functor and two copies of the standard projective functor F is noetherian.
For this, we introduce new categories, the grassmannian functor categories. They permit to formulate a very strong form of the artinian conjecture, describing the Krull filtration of F. Our generalized simplicity theorem allows to show the above result about the structure or P tensor 2 tensor F (with F finite), that we have also proved using internal hom functors and considerations from modular representation theory.
We describe the rich algebraic structure of the grassmannian functor categories, equivalent to comodules categories in F. Our main cohomological vanishing theorem generalizes a lot of known results in functor cohomology. It permits also to generalize a key step in Suslin's proof of the isomorphism between stable K-theory and Mac Lane homology for polynomial coefficients.
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https://tel.archives-ouvertes.fr/tel-00119635
Contributor : Aurélien Djament <>
Submitted on : Monday, December 11, 2006 - 3:18:51 PM
Last modification on : Tuesday, October 20, 2020 - 3:56:35 PM
Long-term archiving on: : Wednesday, April 7, 2010 - 12:23:40 AM

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  • HAL Id : tel-00119635, version 1

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Aurélien Djament. Représentations génériques des groupes linéaires : catégories de foncteurs en grassmanniennes, avec applications à la conjecture artinienne. Mathématiques [math]. Université Paris-Nord - Paris XIII, 2006. Français. ⟨tel-00119635⟩

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