The reductive Borel–Serre compactification as a model for unstable algebraic K-theory
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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.
Original language | English |
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Article number | 10 |
Journal | Selecta Mathematica, New Series |
Volume | 30 |
Issue number | 1 |
Pages (from-to) | 1-93 |
ISSN | 1022-1824 |
DOIs | |
Publication status | Published - 2024 |
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© 2023, The Author(s).
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