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 with the property that has nonzero torsion unless is very special. An important example of such a module is the Frobenius power over a complete intersection domain of characteristic .
"Torsion in tensor powers of modules." Nagoya Math. J. 219 113 - 125, September 2015. https://doi.org/10.1215/00277630-3140827