Noncommutative localization in algebraic L-theory

Andrew Ranicki

doi:10.1016/j.aim.2008.10.003

Noncommutative localization in algebraic L-theory

Andrew Ranicki

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Given a noncommutative (Cohn) localization A -> 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-Ranicki [Amnon Neeman, Andrew Ranicki, Noncommutative localisation in algebraic K-theory I, Geom. Topol. 8 (2004) 1385-1425] and Neeman [Amnon Neeman, Noncommutative localisation in algebraic K-theory II. Adv. Math. 213 (2007) 785-819].

Original language	English
Pages (from-to)	894-912
Number of pages	19
Journal	Advances in Mathematics
Volume	220
Issue number	3
DOIs	https://doi.org/10.1016/j.aim.2008.10.003
Publication status	Published - 15 Feb 2009

Keywords / Materials (for Non-textual outputs)

Noncommutative localization
Chain complexes
L-theory

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10.1016/j.aim.2008.10.003

Noncommutative localization in algebraic L-theory
The final publication is available at ScienceDirect via http://dx.doi.org/10.1016/j.aim.2008.10.003
Submitted manuscript, 179 KB

http://www.sciencedirect.com/science/article/pii/S0001870808002879

Cite this

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AB - Given a noncommutative (Cohn) localization A -> 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-Ranicki [Amnon Neeman, Andrew Ranicki, Noncommutative localisation in algebraic K-theory I, Geom. Topol. 8 (2004) 1385-1425] and Neeman [Amnon Neeman, Noncommutative localisation in algebraic K-theory II. Adv. Math. 213 (2007) 785-819].

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Noncommutative localization in algebraic L-theory

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