On automorphisms of modules over polynomial rings (Q582333)

In the first part, the authors prove the following theorem: Let A be a commutative noetherian ring with \(\dim (A)<+\infty\). Suppose that P is a finitely generated projective \(A[X_ 1,...,X_ n]\)-module such that \(rank(P_ y)>\dim (A)\) for all prime ideals \(y\subset A[X_ 1,...,X_ n]\). Then the natural map \(Aut_{A[X_ 1,...,X_ n]}(P)\to Aut_{A[X_ 1,...,X_{n-1}]}(P/X_ nP)\) is surjective. In particular, for any finitely generated projective A[X]-module P with \(rank(P)>\dim (A)\), the natural map \(Aut_{A[X]}(P)\to Aut_ A(P/XP)\) is surjective. The second part of the paper concerns the acting of some subgroup of \(Aut_{A[X]}(A[X]^ 2\oplus M)\) on the set of all special unimodular elements of \(A[X]^ 2\oplus M\) where M is an A[X]-module.