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arXiv · 2312.09725

An Ext-Tor duality theorem, cohomological dimension, and applications

Rafael Holanda·Cleto B. Miranda-Neto
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Abstract

We provide a duality theorem between Ext and Tor modules over a Cohen-Macaulay local ring possessing a canonical module, and use it to prove some freeness criteria for finite modules. The applications include a characterization of codimension three complete intersection ideals and progress on a long-held multi-conjecture of Vasconcelos. By a similar technique, we furnish another theorem which in addition makes use of the notion of cohomological dimension and is mainly of interest in dimension one; as an application, we show that the celebrated Huneke-Wiegand conjecture in the case of complete intersections holds true provided that a single additional condition is satisfied.

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Rafael Holanda, Cleto B. Miranda-Neto. 2023-12-15. An Ext-Tor duality theorem, cohomological dimension, and applications. https://arxiv.org/abs/2312.09725

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