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Catégories de foncteurs en grassmanniennes

Aurélien Djament
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Abstract

Soit F la catégorie des foncteurs entre espaces vectoriels sur un corps fini. Les catégories de foncteurs en grassmanniennes sont obtenues en remplaçant la source de cette catégorie par la catégorie des couples formés d'un espace vectoriel et d'un sous-espace. Ces catégories possèdent une très riche structure algébrique ; nous étudierons notamment leurs objets finis et leurs propriétés cohomologiques. Nous donnons des applications à la filtration de Krull de la catégorie F et à la K-théorie stable des corps finis. -- Let F be the category of functors between vector spaces over a finite field. The grassmannian functor categories are obtained by replacing the source of this category by the category of pairs formed by a vector space and a subspace. These categories have a very rich algebraic structure; we study in particular their finite objects and their homological properties. We give applications to the Krull filtration of the category F and to the stable K-theory of finite fields.

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Aurélien Djament. 2006-11-07. Catégories de foncteurs en grassmanniennes. https://arxiv.org/abs/math/0610598

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