Structure of A*-fibrations over one-dimensional seminormal semilocal domains

Abstract

In this paper we give a structure theorem for an A*-fibration over a one-dimensional noetherian seminormal semilocal domain and show that, in this situation, any A*-fibration whose spectrum occurs as an affine open subscheme of the spectrum of an A¹-fibration (equivalently, an affine line A¹) is actually A*. The structure theorem provides examples of A-fibrations over one-dimensional noetherian seminormal semilocal domains whose spectra are not affine open subschemes of any affine line A¹ over the base ring. We also construct examples of nontrivial A*-fibrations over one-dimensional noetherian non-seminormal local domains whose spectra are open subschemes of A¹-fibrations over the base ring.