Noncommutative localization in algebraic $L$-theory

Abstract

Given a noncommutative (Cohn) localization $A\to {\sigma }^{-1}A$ which is injective and stably flat we obtain a lifting theorem for induced f.g. projective ${\sigma }^{-1}A$-module chain complexes and localization exact sequences in algebraic $L$-theory, matching the algebraic $K$-theory localization exact sequence of Neeman and Ranicki.

to appear in Advances in Mathematics