K-theory of locally compact modules over orders

被引：2

作者：

Braunling, Oliver ^{[1
]}

Henrard, Ruben ^{[2
]}

Van Roosmalen, Adam-Christiaan ^{[2
]}

机构：

[1] Albert Ludwigs Univ Freiburg, Inst Math, D-79104 Freiburg, Germany

[2] Univ Hasselt, Dept WNI, Campus Diepenbeek, B-3590 Diepenbeek, Belgium

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2021年 / 246卷 / 01期

关键词：

D O I：

10.1007/s11856-021-2247-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a quick approach to computing the K-theory of the category of locally compact modules over any order in a semisimple DOUBLE-STRUCK CAPITAL 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.

引用

页码：315 / 333

页数：19

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