Euler class construction

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=(f1,…,fn-1,fn)+J2. Write I=(f1,…,fn-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]-[Lcircled plusAn-1]=-[A/J]set membership, variantK0(A), (2) P maps onto I and (3) the Euler class e(P,χ)=(I,ω)set membership, variantE(A,L), if A contains the field of rationals.