Cyclic homology of categories of matrix factorizations

@article{Efimov2012CyclicHO,
  title={Cyclic homology of categories of matrix factorizations},
  author={Alexander I. Efimov},
  journal={arXiv: Algebraic Geometry},
  year={2012}
}
  • A. Efimov
  • Published 12 December 2012
  • Mathematics
  • arXiv: Algebraic Geometry
In this paper, we will show that for a smooth quasi-projective variety over $\C,$ and a regular function $W:X\to \C,$ the periodic cyclic homology of the DG category of matrix factorizations $MF(X,W)$ is identified (unde Riemann-Hilbert correspondence) with vanishing cohomology $H^{\bullet}(X^{an},\phi_W\C_X),$ with monodromy twisted by sign. Also, Hochschild homology is identified respectively with the hypercohomology of $(\Omega_X^{\bullet},dW\wedge).$ One can show that the image of the… 
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