The reductive Borel–Serre compactification as a model for unstable algebraic K-theory
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The reductive Borel–Serre compactification as a model for unstable algebraic K-theory. / Clausen, Dustin; Jansen, Mikala Ørsnes.
In: Selecta Mathematica, New Series, Vol. 30, No. 1, 10, 2024, p. 1-93.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The reductive Borel–Serre compactification as a model for unstable algebraic K-theory
AU - Clausen, Dustin
AU - Jansen, Mikala Ørsnes
N1 - Publisher Copyright: © 2023, The Author(s).
PY - 2024
Y1 - 2024
N2 - Let A be an associative ring and M a finitely generated projective A-module. We introduce a category RBS (M) and prove several theorems which show that its geometric realisation functions as a well-behaved unstable algebraic K-theory space. These categories RBS (M) naturally arise as generalisations of the exit path ∞ -category of the reductive Borel–Serre compactification of a locally symmetric space, and one of our main techniques is to find purely categorical analogues of some familiar structures in these compactifications.
AB - Let A be an associative ring and M a finitely generated projective A-module. We introduce a category RBS (M) and prove several theorems which show that its geometric realisation functions as a well-behaved unstable algebraic K-theory space. These categories RBS (M) naturally arise as generalisations of the exit path ∞ -category of the reductive Borel–Serre compactification of a locally symmetric space, and one of our main techniques is to find purely categorical analogues of some familiar structures in these compactifications.
U2 - 10.1007/s00029-023-00900-8
DO - 10.1007/s00029-023-00900-8
M3 - Journal article
AN - SCOPUS:85180491183
VL - 30
SP - 1
EP - 93
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
SN - 1022-1824
IS - 1
M1 - 10
ER -
ID: 377989678