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arXiv · 2502.07483

Higher-dimensional module factorizations and complete intersections

Xiao-Wu Chen
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Abstract

We introduce higher-dimensional module factorizations associated to a regular sequence. They include higher-dimensional matrix factorizations, which are commutative cubes consisting of free modules with edges being classical matrix factorizations. We characterize the stable category of maximal Cohen-Macaulay modules over a complete intersection via higher-dimensional matrix factorizations over the corresponding regular local ring. The result generalizes to noncommutative rings, including quantum complete intersections.

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Xiao-Wu Chen. 2025-02-11. Higher-dimensional module factorizations and complete intersections. https://arxiv.org/abs/2502.07483

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