Vanishing of Euler class groups
Let \(A\) be a noetherian ring and and \(L\) a rank one projective \(A\)-module, and let \(E(A,L)\) denote the Euler class group. This paper contains several results about the vanishing of \(E(A,L)\). One of the main results is as follows. Let \(f\in A[X]\) be a non-zero divisor, and let \(B=A[X,1/f]\), with \(\dim(B)=\dim(A)+1=n\). If \(L\) is a line bundle over \(\text{Spec}(B)\), then the Euler class group \(E(B,L)=0\).
scientific article; zbMATH DE number 5129709