Author:
Clausen Dustin,Jansen Mikala Ørsnes
Abstract
AbstractLet A be an associative ring and M a finitely generated projective A-module. We introduce a category $${\text {RBS}}(M)$$
RBS
(
M
)
and prove several theorems which show that its geometric realisation functions as a well-behaved unstable algebraic K-theory space. These categories $${\text {RBS}}(M)$$
RBS
(
M
)
naturally arise as generalisations of the exit path $$\infty $$
∞
-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.
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,General Mathematics
Reference57 articles.
1. Graduate Texts in Mathematics;P Abramenko,2008
2. Ayala, D., Francis, J.: Fibrations of $$\infty $$-categories. High. Struct. 4(1), 168–265 (2020)
3. Aoki, K.: Tensor triangular geometry of filtered objects and sheaves. Preprint arXiv:2001.00319 (2020)
4. Bullejos, M., Cegarra, A.M.: On the geometry of 2-categories and their classifying spaces. K-Theory 29(3), 211–229 (2003)
5. Barwick, C., Glasman, S., Haine, P.: Exodromy. Preprint arXiv:1807.03281 (2020)