Torsion in tensor products over one-dimensional domains

Neil Steinburg; RogerWiegand

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arXiv · 1902.07157

Torsion in tensor products over one-dimensional domains

Neil Steinburg·RogerWiegand

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Abstract

Over a one-dimensional Gorenstein local domain $R$, let $E$ be the endomorphism ring of the maximal of $R$, viewed as a subring of the integral closure $\overline R$. If there exist finitely generated $R$-modules $M$ and $N$, neither of them free, whose tensor product is torsion-free, we show that $E$ must be local with the same residue field as $R$.

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Neil Steinburg, RogerWiegand. 2019-02-19. Torsion in tensor products over one-dimensional domains. https://arxiv.org/abs/1902.07157

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