FLATNESS TESTING AND TORSION-FREE MORPHISMS

Let psi:A bar arrow pointing right B be a homomorphism of finitely gen erated algebras over a field k or over H. This note is concerned with methods and tools to ascertain whether psi makes B a flat module over A. Morphisms with such properties are very common and desirable in the study of mappings between algebraic varieties. We show how three pill ars of the study, a computable generic flatness, the local criterion a nd tricks in reducing the dimension of the ring, combine to allow for several tests. (C) 1997 Elsevier Science B.V.