The Euler class group of a polynomial algebra

Abstract

In this paper we continue our study on the theory of the Euler class group of a polynomial algebra A[T ], where A is a commutative Noetherian ring (containing Q) of dimension n. For such a ring A, in [9], we defined the notion of the nth Euler class group En(A[T ]) of A[T ]. For simplicity let us call it E(A[T ]). In [9] we also studied the relations between E(A[T ]) and E(A), where E(A) is the nth Euler class group of A. For example, there is canonical map Φ :E(A)→ E(A[T ]) which is an injective group homomorphism and it is an isomorphism when A is a smooth affine domain [9, Proposition 5.7]. In general, these two groups are not isomorphic (see discussion preceding [9, Proposition 5.7]). In this context, the following question is natural.