Noncommutative localization and chain complexes I. Algebraic K- and L-theory
| dc.creator | Neeman, Amnon | |
| dc.creator | Ranicki, Andrew | |
| dc.date | 2001-09-18 | |
| dc.date.accessioned | 2026-07-07T04:43:25Z | |
| dc.date.available | 2026-07-07T04:43:25Z | |
| dc.description | The noncommutative (Cohn) localization S^{-1}R of a ring R is defined for any collection S of morphisms of f.g. projective left R-modules. We exhibit S^{-1}R as the endomorphism ring of R in an appropriate triangulated category. We use this expression to prove that if S^{-1}R is "stably flat over R" (meaning that Tor^R_i(S^{-1}R,S^{-1}R)=0 for i>0) then every bounded f.g. projective S^{-1}R-module chain complex D with [D] \in im(K_0(R)-->K_0(S^{-1}R)) is chain equivalent to S^{-1}C for a bounded f.g. projective R-module chain complex C, and that there is a localization exact sequence in higher algebraic K-theory >... --> K_n(R) --> K_n(S^{-1}R) --> K_n(R,S) --> K_{n-1}(R) --> ..., extending to the left the sequence obtained for n<2 by Schofield. For a noncommutative localization S^{-1}R of a ring with involution R there are analogous results for algebraic L-theory, extending the results of Vogel from quadratic to symmetric L-theory. | |
| dc.description | 75 pages | |
| dc.identifier | https://arxiv.org/abs/math/0109118 | |
| dc.identifier | http://arxiv.org/abs/math/0109118 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62216 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Algebraic Topology | |
| dc.subject | 16S10; 18E30; 19D50; 57R67 | |
| dc.title | Noncommutative localization and chain complexes I. Algebraic K- and L-theory | |
| dc.type | text |