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Localization and completion in L-theory

  • Andrew Ranicki
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

Localization and completion techniques are a standard feature of the theory of quadratic forms, as evidenced by the Hasse-Minkowski local-global principle. Refer to Chap. 3 of Ranicki [237] for an account of the relevant L-theory. The main novelty here is that the localization exact sequences of [237] in є-symmetric and є-quadratic L-theory
$$\begin{array}{*{20}{c}} { \ldots \to {{L}^{n}}\left( {A, \in } \right) \to {{L}^{n}}\left( {{{S}^{{ - 1}}}A, \in } \right) \to {{L}^{n}}\left( {A,S, \in } \right) \to {{L}^{{n - 1}}}\left( {A, \in } \right) \to \ldots ,} \\ { \ldots \to {{L}_{n}}\left( {A, \in } \right) \to {{L}_{n}}\left( {{{S}^{{ - 1}}}A, \in } \right) \to {{L}_{n}}\left( {A,S, \in } \right) \to {{L}_{{n - 1}}}\left( {A, \in } \right) \to \ldots } \\ \end{array}$$
are extended to noncommutative localizations Σ −1 A of a ring with involution A.

Keywords

Exact Sequence Invariant Subgroup Exact Category Witt Group Completion Technique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Andrew Ranicki
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of EdinburghEdinburghScotland, UK

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