On Gorenstein fiber products and applications
arXiv preprint arXiv:1701.08689, 2017•arxiv.org
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.
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.
We show that a non-trivial fiber product of commutative noetherian local rings with a common residue field is Gorenstein if and only if it is a hypersurface of dimension 1. In this case, both and are regular rings of dimension 1. We also give some applications of this result.
arxiv.org
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