论文标题
在本地Finte类别的K_0上
On K_0 of locally finte categories
论文作者
论文摘要
我们计算Grothendieck组$ k_0（\ cal a）$，其中$ \ cal a $是一个加性类别，在Dedekind环上本地有限，并满足了一些其他条件。主要示例是有限代数上的模块类别和稳定的同型类别$ \ mathsf {sw} $的有限cw-complexes。我们表明，该组是由类别$ \ cal a $的本地化和类似于理想类别最大订单的组类似的群体的直接总和。作为推论，我们获得了弗雷德定理的新简单证明，描述了组$ k_0（\ mathsf {sw}）$。
We calculate the Grothendieck group $K_0(\cal A)$, where $\cal A$ is an additive category, locally finite over a Dedekind ring and satisfying some additional conditions. The main examples are categories of modules over finite algebras and the stable homotopy category $\mathsf{SW}$ of finite CW-complexes. We show that this group is a direct sum of a free group arising from localizations of the category $\cal A$ and a group analogous to the groups of ideal classes of maximal orders. As a corollary, we obtain a new simple proof of the Freyd's theorem describing the group $K_0(\mathsf{SW})$.
