1. $K$-theory of locally compact modules over orders
- Author
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Adam-Christiaan van Roosmalen, Oliver Braunling, Ruben Heradio, Braunling, Oliver, VAN ROOSMALEN, Adam-Christiaan, and HENRARD, Ruben
- Subjects
Mathematics - Number Theory ,General Mathematics ,19B28, 19F05, 22B05, 18E35 ,Mathematics - K-Theory and Homology ,FOS: Mathematics ,K-Theory and Homology (math.KT) ,Number Theory (math.NT) - Abstract
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., Comment: 8 pages. Comments welcome