2021/08/04 by Dustin Clausen, Mikala Ørsnes Jansen, Clausen, Dustin +1 · 4 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2108.01924
openalex publication_date 2021/08/04 · openalex created_date 2022/07/25 · openalex updated_date 2026/08/01
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.