Burke, JesseWalker, Mark2018-11-292018-11-291532-0073http://hdl.handle.net/1885/153129We study matrix factorizations of regular global sections of line bundles on schemes. If the line bundle is very ample relative to a Noetherian affine scheme we show that morphisms in the homotopy category of matrix factorizations may be computed as the hypercohomology of a certain mapping complex. Using this explicit description, we prove an analogue 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. Moreover, we give a complete description of the image of this functor.application/pdf201210.4310/HHA.2012.v14.n2.a32018-11-29