Structure of A*-Fibrations over One-Dimensional Seminormal Semilocal Domains

✍ Scribed by S.M. Bhatwadekar; Amartya K. Dutta

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 117 KB
• Volume: 220
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.8182

✦ Synopsis

In this paper we give a structure theorem for an A * -fibration over a onedimensional 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 A 1 -fibration (equivalently, an affine line A 1 ) 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 A 1 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 A 1 -fibrations over the base ring.