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arXiv · 2606.32031

Intersection theorems over DG-rings revisited

Luigi Ferraro·Zachary Nason
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Abstract

In this work we generalize two recently proved intersection theorems for DG-rings. The Derived Improved New Intersection Theorem concerns the length of semi-free DG-modules over DG-rings and it was recently proved by the second author. We show that it holds under weaker hypotheses. Foxby's Intersection Theorem was generalized to DG-rings by Yang and we improve the inequality that they provided. As an application we prove a DG version of the classic result that finite length modules of finite projective dimension only exist over Cohen-Macaulay rings, generalizing another result of Yang.

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Luigi Ferraro, Zachary Nason. 2026-06-30. Intersection theorems over DG-rings revisited. https://arxiv.org/abs/2606.32031

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