Localization and completion in L-theory

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


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.


Exact Sequence Invariant Subgroup Exact Category Witt Group Completion Technique 
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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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