Excision in algebraic obstruction theory

Abstract

In this paper the relative algebraic obstruction groups (also known as Euler class groups) were defined and some excision exact sequences were established. In particular, for a regular domain A, essentially of finite type over an infinite field k, and a rank one projective A-module L0, it was proved that En(A[T],L0⊗A[T])≈En(A,L0)whenever 2n≥dimA+4.