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 languageEnglish
Article number10
JournalSelecta Mathematica, New Series
Issue number1
Pages (from-to)1-93
Publication statusPublished - 2024

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© 2023, The Author(s).

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