Grassmann 流形上的函子范畴

设 F 为有限域上向量空间之间的函子范畴。Grassmann 流形上的函子范畴是通过将该范畴的源替换为由一个向量空间及其子空间组成的对构成的范畴而得到的。这些范畴具有非常丰富的代数结构；我们特别研究其有限对象与上同调性质。我们给出了对范畴 F 的 Krull 滤过以及有限域的稳定 K-理论的应用。——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.