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arXiv · 2201.11955

Openness of various loci over Noetherian rings

Kaito Kimura
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Abstract

In this paper, we consider the openness of the P-locus of a finitely generated module over a commutative noetherian ring in the case where P is each of the properties FID, Gor, CM, MCM, (S_n), and (T_n). One of the main results asserts that FID-loci over an acceptable ring are open. We give a module version of the Nagata criterion, and prove that it holds for all of the aforementioned properties.

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Kaito Kimura. 2022-01-28. Openness of various loci over Noetherian rings. https://arxiv.org/abs/2201.11955

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