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The L-theory of Laurent extensions and genus 0 function fields. (English) Zbl 0692.13010

An exact sequence expresses the L-groups of the Laurent extension \(A[t,t^{-1}]\) of a ring with involution A in terms of the L-groups of A, where the involution \(a\to \bar a\) on A is extended by \(\bar t=ut^{- 1}\) for some unit u of A with \(\bar u=u\). The exact sequence is used to compute the Witt groups of quadratic forms in genus 0 function fields, over fields of characteristic \(\neq 2\).
Reviewer: R.J.Milgram

MSC:

13D15 Grothendieck groups, \(K\)-theory and commutative rings
13F25 Formal power series rings
11E16 General binary quadratic forms
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
11E12 Quadratic forms over global rings and fields
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