The reductive Borel–Serre compactification as a model for unstable algebraic K-theory

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.

Funder

Copenhagen University

Publisher

Springer Science and Business Media LLC

Subject

General Physics and Astronomy,General Mathematics

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