Abstract
Suppose A is a commutative noetherian ring of dimension n , and L is a line bundle on Spec ( A ) . Suppose J is a local complete intersection ideal of height n and J = ( f 1 , … , f n - 1 , f n ) + J 2 . Write I = ( f 1 , … , f n - 1 ) + J ( n - 1 ) ! . Let ( I , ω ) be any L-cycle in the Euler class group E ( A , L ) . We construct an oriented projective A-module ( P , χ ) such that (1) [ P ] - [ L ⊕ A n - 1 ] = - [ A / J ] ∈ K 0 ( A ) , (2) P maps onto I and (3) the Euler class e ( P , χ ) = ( I , ω ) ∈ E ( A , L ) , if A contains the field of rationals.
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