Torsion in tensor powers of modules

Abstract

Tensor products usually have nonzero torsion. This is a central theme of Auslander’s 1961 paper; the theme continues in the work of Huneke and Wiegand in the 1990s. The main focus in this article is on tensor powers of a finitely generated module over a local ring. Also, we study torsion-free modules $N$ with the property that $M{\otimes }_{R}N$ has nonzero torsion unless $M$ is very special. An important example of such a module $N$ is the Frobenius power ${}^{p^e}R$ over a complete intersection domain $R$ of characteristic $p>0$.