Torsion in tensor powers of modules

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 circle times(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.