Flatness testing and torsionfree morphisms Original Research Article

Let ψ : A maps to B be a homomorphism of finitely generated algebras over a field k or over image. This note is concerned with methods and tools to ascertain whether ψ 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 pillars of the study, a computable generic flatness, the local criterion and tricks in reducing the dimension of the ring, combine to allow for several tests.