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Higher-dimensional module factorizations and complete intersections (2502.07483v2)
Published 11 Feb 2025 in math.RA, math.AC, and math.RT
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.