**Memoires de la Societe Mathematique de France**

Volume: 111;
2007;
213 pp;
Softcover

MSC: Primary 16; 18; 20; 19; 55;
**Print ISBN: 978-2-85629-248-8
Product Code: SMFMEM/111**

List Price: $55.00

Individual Member Price: $44.00

# Foncteurs en Grassmanniennes, Filtration de Krull et Cohomologie des Foncteurs

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*Aurélien Djament*

A publication of the Société Mathématique de France

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.

#### Readership

Graduate students and research mathematicians interested in algebra and algebraic geometry.