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Mémoires de la Société Mathématique de France
2007; 213 pp; softcover
List Price: US$55
Individual Members: US$49.50
Order Code: SMFMEM/111
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 an element of one of its grassmannians. These categories have a very rich algebraic structure; the author studies in particular their finite objects and their homological properties.
The author gives a very general vanishing property in functor cohomology, which he applies to the stable \(K\)-theory of finite fields: He obtains a generalization of the Betley-Suslin theorem, which expresses certain extension groups of \(GL_\infty\)-modules in terms of functor cohomology.
The author's second application of the grassmannian functor categories concerns the Krull filtration of the category \(F\). He gives a conjectural description of this filtration and explores its powerful implications. With the help of tools provided by G. Powell, the author shows a weak form of this conjecture, in the case where the basis field has two elements. Consequently, he establishes the noetherian character of new functors.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians interested in algebra and algebraic geometry.
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