Abstract
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.
| Originalsprog | Engelsk |
|---|---|
| Artikelnummer | 10 |
| Tidsskrift | Selecta Mathematica, New Series |
| Vol/bind | 30 |
| Udgave nummer | 1 |
| Sider (fra-til) | 1-93 |
| ISSN | 1022-1824 |
| DOI | |
| Status | Udgivet - 2024 |
Bibliografisk note
Funding Information:Both authors were supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and the Copenhagen Centre for Geometry and Topology (DNRF151). MJ was also supported by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant Agreement No. 682922).
Publisher Copyright:
© 2023, The Author(s).