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arXiv · 2405.00240

Intersection Theorem for DG-modules

Xiaoyan Yang
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Abstract

Let A be a commutative noetherian local DG-ring with bounded cohomology. The Intersection Theorem for DG-modules is examined and some of its applications are provided. The first is to prove the DG-setting of the amplitude inequality, New Intersection Theorem and Krull's principle ideal theorem. The second is to solve completely the Minamoto's conjecture in [Israel J. Math. 242 (2021) 1-36]. The third is to show the DG-version of the Bass conjecture about Cohen-Macaulay rings and the Vasconcelos conjecture about Gorenstein rings.

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Xiaoyan Yang. 2024-04-30. Intersection Theorem for DG-modules. https://arxiv.org/abs/2405.00240

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