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arXiv · 1710.07398

On the ideal case of a conjecture of Huneke and Wiegand

Olgur Celikbas·Shiro Goto·Ryo Takahashi·Naoki Taniguchi
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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.

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Olgur Celikbas, Shiro Goto, Ryo Takahashi, Naoki Taniguchi. 2018-09-20. On the ideal case of a conjecture of Huneke and Wiegand. https://doi.org/10.1017/s0013091518000731

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