TY - JOUR
T1 - K-theory of locally compact modules over orders
AU - Braunling, Oliver
AU - Henrard, Ruben
AU - van Roosmalen, Adam Christiaan
N1 - Publisher Copyright:
© 2021, The Hebrew University of Jerusalem.
PY - 2021/12
Y1 - 2021/12
N2 - We present a quick approach to computing the K-theory of the category of locally compact modules over any order in a semisimple 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.
AB - We present a quick approach to computing the K-theory of the category of locally compact modules over any order in a semisimple 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.
UR - http://www.scopus.com/inward/record.url?scp=85115671438&partnerID=8YFLogxK
U2 - 10.1007/s11856-021-2247-5
DO - 10.1007/s11856-021-2247-5
M3 - Article
AN - SCOPUS:85115671438
SN - 0021-2172
VL - 246
SP - 315
EP - 333
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -