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

• Dustin Clausen ^[1] ; Mikala Ørsnes Jansen ^[1]
  1. [1] University of Copenhagen

     University of Copenhagen

     Dinamarca

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 1, 2024, págs. 1-93
• Idioma: inglés
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• Resumen

  • 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