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arXiv · 1701.08689

On Gorenstein fiber products and applications

Saeed Nasseh·Ryo Takahashi·Keller VandeBogert
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Abstract

We show that a non-trivial fiber product $S\times_k T$ of commutative noetherian local rings $S,T$ with a common residue field $k$ is Gorenstein if and only if it is a hypersurface of dimension 1. In this case, both $S$ and $T$ are regular rings of dimension 1. We also give some applications of this result.

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Saeed Nasseh, Ryo Takahashi, Keller VandeBogert. 2018-02-02. On Gorenstein fiber products and applications. https://arxiv.org/abs/1701.08689

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