If E and F are reflexive sheaves of rank one， is their tensor product $E\otimes F$ reflexive？ Thanks！
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Let $R=k[[x,y]]/(xy)$ be the node and $I=(x,y)$ the maximal ideal. Then $I$ is reflexive of rank $1$, but the tensor product $I \otimes_{R} I$ is not reflexive. Indeed, the self-tensor product admits the nonzero torsion section $x \otimes y$. |
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