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Regular version of the site

Article

Cyclic homology of categories of matrix factorizations

International Mathematics Research Notices. 2018. No. 12. P. 3834-3869.

In this article, we will show that for a smooth quasi-projective variety X over complex numbers, and regular function  W on X, the periodic cyclic homology of the DG category of matrix factorizations of W on X is identified (under the Riemann–Hilbert correspondence) with the vanishing cohomology, with the monodromy twisted by a sign. Also, Hochschild homology is identified respectively with the hypercohomology of the complex of differential forms, with a differential being a wedge product with dW.