Torsion in Tensor Products over One-Dimensional Domains

Abstract

Over a one-dimensional Gorenstein local domain R, let E be the endomorphism ring of the maximal of R, viewed as a subring of the integral closure R. If there exist finitely generated R-modules M and N , neither of them free, whose tensor product is torsion-free, we show that E must be local with the same residue field as R.