论文标题
$ k $ - 订单上本地紧凑模块的理论
$K$-theory of locally compact modules over orders
论文作者
论文摘要
我们提出了一种快速方法，用于计算$ k $ - 在半imimple $ \ mathbb {q} $ - 代数中以任何顺序计算本地紧凑模块类别的理论。我们首先介绍紧凑型模块，然后再进行矢量模块，从而获得$ k $ - 理论。我们的证明利用了这对（向量模块加紧凑模块，离散模块）成为扭转理论的事实。由于最近的本地化形式主义，可以将这些商视为确切类别。
We present a quick approach to computing the $K$-theory of the category of locally compact modules over any order in a semisimple $\mathbb{Q}$-algebra. We obtain the $K$-theory by first quotienting out the compact modules and subsequently the vector modules. Our proof exploits the fact that the pair (vector modules plus compact modules, discrete modules) becomes a torsion theory after we quotient out the finite modules. Treating these quotients as exact categories is possible due to a recent localization formalism.
