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arXiv · 1110.2918

Matrix factorizations over projective schemes

Jesse Burke·Mark E. Walker
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Abstract

We study matrix factorizations of locally free coherent sheaves on a scheme. For a scheme that is projective over an affine scheme, we show that homomorphisms in the homotopy category of matrix factorizations may be computed as the hypercohomology of a certain mapping complex. Using this explicit description, we give another proof of Orlov's theorem that there is a fully faithful embedding of the homotopy category of matrix factorizations into the singularity category of the corresponding zero subscheme. We also give a complete description of the image of this functor.

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Jesse Burke, Mark E. Walker. 2012-05-11. Matrix factorizations over projective schemes. https://arxiv.org/abs/1110.2918

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