On the ideal case of a conjecture of Huneke and Wiegand

Abstract

A conjecture of Huneke and Wiegand claims that, over one-dimensional commutative Noetherian local domains, the tensor product of a finitely generated, non-free, torsion-free module with its algebraic dual always has torsion. Building on a beautiful result of Corso, Huneke, Katz and Vasconcelos, we prove that the conjecture is affirmative for a large class of ideals over arbitrary one-dimensional local domains. Furthermore we study a higher dimensional analog of the conjecture for integrally closed ideals over Noetherian rings that are not necessarily local. We also consider a related question on the conjecture and give an affirmative answer for first syzygies of maximal Cohen-Macaulay modules.

10 pages and to appear in Proceedings of the Edinburgh Mathematical Society

References in corpus (2)

• Homological dimensions of rigid modules
• On the second rigidity theorem of Huneke and Wiegand

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• On a class of Burch ideals and a conjecture of Huneke and Wiegand
• Stable trace ideals and applications
• A study of the cohomological rigidity property
• On the vanishing of (co)homology for modules admitting certain filtrations
• On the ideal case of a conjecture of Auslander and Reiten