Matrix factorizations in higher codimension

Burke, Jesse; Walker, Mark

doi:10.1090/S0002-9947-2015-06323-5

Matrix factorizations in higher codimension
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by Jesse Burke and Mark E. Walker PDF

Trans. Amer. Math. Soc. 367 (2015), 3323-3370 Request permission

Abstract:

We observe that there is an equivalence between the singularity category of an affine complete intersection and the homotopy category of matrix factorizations over a related scheme. This relies in part on a theorem of Orlov. Using this equivalence, we give a geometric construction of the ring of cohomology operators, and a generalization of the theory of support varieties, which we call stable support sets. We settle a question of Avramov about which stable support sets can arise for a given complete intersection ring. We also use the equivalence to construct a projective resolution of a module over a complete intersection ring from a matrix factorization, generalizing the well-known result in the hypersurface case.

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